All Sub Ques

P E S Institute of Technology – Education for the Real World – Course Information – B.E. 3rd Semester CS - 1 -

GENERAL GUIDELINES • This book is to be brought to the class daily. • Students are not permitted to attend the class without the identity card. • Students should be well in time for the first class and subsequent classes thereafter. • Students should keep the Classrooms, Laboratories and Workshops clean and tidy. • Writing on desks, walls is strictly prohibited, failing which the students will be fined a heavily. If the identity of the individual is

not established the entire class / students in the block will be fined. • Students are advised to show due respect to all faculty regardless of their department and maintain affable personality. • Students are to maintain absolute discipline and decorum, so as to promote the fair name of the college in all its activities. • Students securing less than 85% attendance in any individual subject in the semester will not be allowed to take up the exams.

Attendance and the test performance will be announced in the concerned depart notice board as per the calendar of events and the students are advised to bring any discrepancy to the notice of the HOD.

• Students are informed to clarify their doubts in the respective subjects with the faculty by taking prior appointment. • Students are to inform their parents that they should follow up the progress of their wards by being in touch with the college authorities at

regular intervals.

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• Students should come prepared with algorithm / flowchart / program for all the experiments before attending the laboratory session.

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SEMESTER - III - TIME TABLE Day / Time 8.15 - 9.15 9.15 - 10.15 10.45 –11.45 11.45-12.45 1.30-2.30 2.30-3.30 3.45-4.45 4.45-5.45 Monday Tuesday Wednesday Thursday Friday Saturday

SCHEME OF STUDY AND EXAMINATIONS FOR BE DEGREE COURSE IN COMPUTER SCIENCE & ENGINEERING

No. of Hr. / week Duration of Exams Sl. No

Code No. Subject Theory Practical Theory Practical

Class Sessional

Marks Exam Marks Total Marks

1. 06MAT31 Maths III 04 -- 03 -- 25 100 125 2. 06CSE32 Electronic Circuits 04 -- 03 -- 25 100 125 3. 06CSE33 Logic Design 04 -- 03 -- 25 100 125 4. 06CSE34 Discrete Mathematical

Structures 04 -- 03 -- 25 100 125

5. 06CSE35 Data Structures with C 04 -- 03 -- 25 100 125 6. 06CSE36 Unix & Shell

Programming 04 -- 03 -- 25 100 125

7. 06CSEL37 Data Structures Lab -- 03 -- 03 25 50 75 8. 06CSEL38 Electronic Circuits &

Logic Design Lab -- 03 -- 03 25 50 75

Total 24 06 - - 200 700 900 STUDENT SELF APPRAISAL

MARKS ATTENDANCE SUBJECT TEST 1 TEST 2 TEST 3 REPORT 1 REPORT 2 REPORT 3

Maths III Electronic Circuits Logic Design Discrete Mathematical Structures

Data Structures with C Unix & Shell Programming

Data Structures Lab Electronic Circuits & Logic Design Lab

SMILE AND BE PROUD OF BEING A PART OF P.E.S.I.T FAMILY


06MAT 31 - ENGINEERING MATHEMATICS-III

Faculty: No. of Hours: 52

% of Portion Covered

Class #

Chapter Title / Reference Literature

Topics to be Covered Referen

ce Chapter

Cumulative

1 Fourier Series- Periodic Functions 2 Fourier Expansions 3 Half Range Expansions 4 Complex form of Fourier Series 5 Practical Harmonic Analysis 6

Chapter 10: Fourier Series 10.1 to 10.7, 10.10,10.11 Chapter22: Integral Transforms 22.4, 22.5

Finite and Infinite Fourier Transforms

11.5% 11.5%

7 Fourier sine and cosine transforms 8 Properties, inverse transforms 9 Partial Differential Equations- Formation of PDE 10 Equations Solvable by Direct Integration 11 Solution of homogeneous PDE 12 Method of separation of variables 13 Solution of Lagrange’s linear PDE 14 Derivation of one dimensional wave and heat equations 15 Solution by the method of separation of variables 16 D’ Alembert’s solution of wave equation 17 Two dimensional Laplace’s equation and various possible

solutions 18

Chapter17: Partial Differential Equations 17.1 to 17.5 Chapter18: Applications of PDE 18.4, 18.5, 18.7

Boundary value problems

23 %

34.6 %

19 Numerical Methods- Solution of algebraic and transcendental equations

20 Solution of linear simultaneous equations

21 Eigen values and eigen vectors

22

Chapter24: Numerical Methods 24.1, 24.2, 24.4 to 24.6. 24.8 Chapter25: Finite differences and Interpolation 25.1, 25.5, 25.12 to 25.14, 25.16

Rayleigh’s power method

7.6 %

42.2%

23 Finite Differences-Forward and backward 24 Newton’s Interpolation formulae 25 Newton’s divided difference formula 26 Lagrange’s Interpolation formulae 27 Numerical differentiation using Newton’s formulae 28 Numerical Integration 29 Calculus of Variations- Variation of a function and a

functional, Extremal of a functional 30 Euler’s equation and its solutions 31 Geodesics, minimal surface of revolution, hanging chain and

Brachistochrone problems 32

Chapter 30: Calculus of Variations 30.1 to 30.5 Chapter 26: Difference Equations and Z-Transforms 26.1, 26.2, 26.9to 26.15, 26.20, 26.21

Difference Equations – Basic Definitions

19.2 %

61.4 %


33 Z–Transforms: Definition and Standard Z–Transforms

34 Properties of Z–Transforms 35 Initial and Final value theorems 36 Inverse Z-Transforms 37 Application of Z-Transforms to solve Difference equations 38 Fourier Series- Periodic Functions 39 Fourier Expansions 40 Half Range Expansions 41

Chapter 10: Fourier Series 10.1 to 10.7, 10.10,10.11 Chapter22: Integral Transforms 22.4, 22.5 Complex form of Fourier Series

17.3 %

78.7%

42 Practical Harmonic Analysis 43 Finite and Infinite Fourier Transforms 44 Fourier sine and cosine transforms 4 Properties, inverse transforms 46 Partial Differential Equations- Formation of PDE 47

Chapter17: Partial Differential Equations 17.1 to 17.5 Chapter18: Applications of PDE 18.4, 18.5, 18.7

Equations Solvable by Direct Integration

11.53 % 90.23 %

48 Solution of homogeneous PDE 49 Method of separation of variables 50 Solution of Lagrange’s linear PDE 51 Derivation of one dimensional wave and heat equations 52

Solution by the method of separation of variables

9.77 % 100%

Literature:

Publication info Book Type

Code

Author & Title Edition Publisher Year

Text book T1 Higher Engineering Mathematics by Dr.B.S.Grewal 36th Khanna,New

Delhi 2002

References

R1 Higher Engineering Mathematics by B. V. Ramana Tata-McGraw

Hill

Reference R2 Advanced Modern Engineering Mathematics by Glyn James Pearson

Syllabus for test :

Test # Syllabus

T1 Class # 01 to 17

T2 Class # 18 to 34

T3 Class # 35 to 52


QUESTION BANK

PART A

Unit I: Fourier Series

I Obtain the Fourier series expansion for the following functions in the given intervals: 1 e-x in ( -π , π ).

2 x2 in ( -π , π ) and hence deduce that ∑= 2

2 16 n

π

3 x – 1 in ( -π , π ). 4 x in ( -1, +1 ). 5 x – x2 in ( -1, +1 ). 6 π 2 – x2 in ( -π , π ). 7 x( 2π - x) in ( 0, 2π ). 8 2x – x2 in ( 0, 3 ). 9 ⎢x ⎢ in ( -π , π ). Hence deduce the value of π2/8

10 x sinx in (0, 2π) and hence deduce that π = 1 +2 [ 1 – 1 + 1_ - + - - - - -] 2 3 3.5 5.7

11 x2 in ( 0, 2π ) and hence deduce that π2 = 1 + 1 + 1 + . . . . . . . . . and π2 = 1 - 1 + 1 - . . . . . . .

6 12 22 32 12 12 22 32

12 x3 in ( -π, π ). 13 1 – x + x2 in ( -π, π ). 14 ( x - π )2 in ( 0, 2π ). 15 e-ax in ( -π, π ). Hence obtain the series for __π__

sinh x 16 1 + x , -π ≤ x ≤ 0

f (x) = 1 - x , 0 ≤ x ≤ π

17 π, -π ≤ x ≤ 0 f (x ) = x , 0 ≤ x ≤ π

18 -k , - π ≤ x ≤ 0 f(x) = k, 0 ≤ x ≤ π

19 x , 0 ≤ x ≤ k f(x) = x – 2k, k ≤ x ≤ 2k

20 x2 , 0 ≤ x ≤ π f(x) = -( 2π - x)2 π ≤ x ≤ 2π

21 πx, 0 ≤ x ≤ 1 f(x) = π ( 2 – x ) 1 ≤ x ≤ 2

22 x, 0 ≤ x ≤ π f(x) = 2π - x, π ≤ x ≤ 2π Hence deduce that π2 = 1 + 1 + 1 + - - - - - - 8 12 32 52

23 2, -2 ≤ x ≤ 0 f(x) = x, 0 ≤ x ≤ 2

II Find the half - range cosine and half - range sine series for the following.


( a ). f (x) = x ( π - x ) in ( 0, π ). ( b ) f (x ) = x2 in ( 0, π ). 2k x, ( 0, 1/2 ) (c ) f (x ) = 2k (1 - x ), ( 1/2, 1 )

III Find the half -range cosine series for the following: (a) f (x ) = x in ( 0, 2 )

(b) f (x ) = (x - 1 )2 in ( 0, 1 )

x, 0 ≤ x ≤ 1 (c) f (x) = 2 - x, 1 ≤ x ≤ 2 Cosx , 0 ≤ x ≤ π/2 (d) f (x) = 0, π/2 ≤ x ≤ π

IV Find the half - range sine series for the following: (a) f (x) = x3 in ( 0, 2 )

(b) f (x) = 1+x2 in ( 0, π )

(1/4) - x, in ( 0, 1/2 ) (c) f (x) = x - (3/4), in ( 1/2, 1 ) cosx, 0 ≤ x ≤ π/4 (d) f (x) = sinx, π/4 ≤ x ≤ π/2

V Expand y in terms of Fourier series using the table below.

x: 0 π /6 π/3 π/2 2π/3 5π /6

Y: 0 9.2 14.4 17.8 17.3 11.7 VI Determine the Fourier expansion, up to the three harmonics, for the function f(θ) defined by the

following table.

θ0 30 60 90 120 150 180 210 240 270 300 330 360

f(θ) 0.6 0.83 1.0 0.8 0.42 0 -0.34 -0.5 -0.2 0.67 0.7 0.5

VII The turning moment T on the crank-shaft of a steam engine for crank angle degrees

is given below:

θ: 0 15 30 45 60 75 90 105 120 135 150 165

T: 0 2.7 5.2 7.0 8.1 8.3 7.9 6.8 5.5 4.1 2.6 1.2

Express T in sine series up to second harmonics. Unit II : Fourier Transforms

1 Define the Fourier transform of a function f(x) and give the inversion formula. Use ‘α’ as the parameter.

2 Find the F.T. of the functions defined as follows: eiikx, a<x<b


(a) f(x) = 0, otherwise 1 - x2, ⎢x⎥ < 1 (b) f(x) = 0, otherwise 1 - ⎢x⎥ , ⎢x⎥ < a (c) f(x) = Hence show that sin2 t dt = π 0, ⎢x⎥ >a t2 2 0, x<p (d) Show that the F.T. of f(x) = 1, p<x<q is 1/√2π eiqα - eipα 0, x>q iα √2π , ⎢x⎥ < a (e) f(x) = 2a 0, otherwise (f) f(x) = ⎢x⎥ e- a ⎢x⎥ , ‘a’ is a positive constant

3 (a2 - x2)-1/2 , ⎢x⎥ < a Show that F.T. of f(x) = is √π/2 J0(aα)

0, otherwise

4 Show that the F.T. of the Dirac-delta function δ(x - a) is 1/√2π eiαa 5 Show that the function e-x/2 is self reciprocal with respect to the F.T. by finding the

F.T. of e-a x , a>0 6 Find the F.T. of (i) x sin 4x2 (ii) x2e-4x

(iii) The Heaviside Unit Step function H(x - a) using δ(x - a) = H’(x - a) 7 Find the Fourier Cosine and Fourier sine transforms of e-ax, a>0. Hence deduce the inversion

formulae.

8 Find the Fourier Cosine transforms of :

(i) e-x (ii) 1 (iii) x2e-ax (iv) e-ax 1+x2 x (v) cosx, 0<x<a f(x) = 0, x ≥ a

9 Find the Fourier Sine transforms of : (i) e-x (ii) x (iii) xe-ax (iv) e-ax (v)f(x) = sinx, 0<x<a 1+x2 x 0, x ≥ a

10 Find Fc(α) and Fs(α) of f(x) =

⎩⎨⎧

≥<<

axax

,00,1

11 Find the F.S.T. of e- ⎢x ⎟ and hence deduce that ∫

∞−=

+0

m2 e

2πdxsinmx

x1x

12 Find f(x) if its sine transform is e-aα. Hence find the inverse sine transform of 1 . α α

13 Find the Fourier Sine and Cosine transforms of xm-1, 0<m<1.


Unit III : Partial Differential Equations

1 Form the P.D.E by eliminating the arbitrary constants from the following relations: _________ (a) z = xy + y √ x2 - a2 + b (b) z = a x ey + (1/2)a2 e2y + b (c) x2 + y2 + z2 = 1 (d) z= (x-a) 2 + (y-b) 2

a2 b2 c2

2 Form the P.D.E by eliminating the arbitrary functions in the following relations: (a) xy + yz + zx = f (z/(x + y)) (b) x + y + z = f (x2 + y2 + z2 ) (c) z = f (x) + ey g (x) (d) x = f (z) + g (y). (e) ax + by + cz = f (x2 + y2 +z2) (f) z = f (x+ay) + φ (x-ay) (g) z = y 2 + 2f (1/x + log y).

3 (a) Find the P.D. E of all spheres of radii ‘r’ and centers on the plane z = 0. (b) Find the P.D. E of all planes which are at a constant distance p from the origin.

4 Solve the following linear P.D.E s: (a) p - 2q = 2x - ey + 1 (b) x( y - z) p + y( z - x) q = z(x - y) (c) x2p + y2q = (x + y) z (d) p + q = x + y + z (e) z(p - q) = x + y + z (f) z(p x - q y) = y2 - x2 (g) (x + 2z) p + (4zx - y) q = 2x2 + y (h) ( x 2 - y z) p + ( y 2 – z x) q = z 2 -x y (i) p z x + q x y = x y

5 Solve the following nonlinear P.D.E .s: (a) y p + x q = p q using u = x2, v = y2 (b) x2y3z6 = p q using u = (x3/3), v = (y4/4), w = - (1/2z2) (c) x2 p2 + y2 q2 = z using u = log x, v = log y (d) q2 y2 = z(z – p x) using u=log x, v=log y and find the singular solution if it exists. (e) z2 (p2 z2 + q2) = 1 and find the singular solution if it is exists. (f) p2+ q2= z2 (x2 + y2) using w = log z and find the singular solution if it exists. (g) ( x -y ) ( p x – q y) = ( p - q) 2 .[ Use x+y = u , x y = v]

6 Solve the following equations by the method of separation of variables: (a) py3 + qx2 = 0 (b) ∂u = 2∂u + u, where u (x,0) = 6e-3x

∂x ∂t (c) 4∂u + ∂u = 3u, given u = 3e-y –e-5y when x = 0

∂x ∂y 7

Solve 0)2sin(18 22

3

=−++∂∂

∂ yxxyyx

z by direct integration.

8 Solve 02

2

=+∂∂ zxz

given that when x = 0, z= ey and 1=∂∂xz

by direct integration.

9 Solve 02

2

=−∂∂ xyxz

by direct integration.

Unit IV : Applications of Partial Differential Equations

1 Solve completely the equation ∂2y/∂t2 = c2 ∂2y/∂x2, representing the vibrations of a string of length l, fixed at both the ends, given that y(0,t) =0; y(x,0) = f(x) and ∂y (x,0) / ∂t =0, 0<x<l.

2 A tightly stretched string with fixed end points x = 0 and x = l is initially in a position given by y = yo Sin3 (πx / l). If it is released from rest from this position, find the displacement y(x,t).


3 A homogeneous rod of conducting material of length 100 cm has its ends kept at zero temperature and the temperature initially is

x , 0 ≤ x ≤ 50 u(x,0) =

100-x , 50 ≤ x ≤ 100. Find the temperature u (x, t) at any time t.

4 Solve ut = 4uxx subject to the conditions, u(0,t) = 0 for all t; u(1,t) = 0 ; u(x,0) = x - x2 (0 ≤ x ≤ 1).

5 A string is stretched and fastened to two points at a distance ‘l’ apart. Motion is started by displacing the string into the form, y = k( lx - x2 ) from which it is released at time t = 0 Find the displacement of any point on the string at a distance x from one end at time t.

PART B Unit V: Numerical Methods

1 Use Bisection method to find a real root of the following equations:

1. x3-2x-5= 0 in 5 stages

2. x log10 x=1.2 between 2 & 3 up to 3 decimal places

3. x3-5x-4= 0 in the range (2,3)

4. x3-3x-5= 0 in the range (2,2.5) correct to 2 decimal places

2 Use Regular – Falsi method to find a real root of the following equation:

1. sinx- coshx+ 1= 0

2. x2- logex –12 = 0

3. cosx- 3x+1= 0

4. ex-3x= 0

5. x4+ 2x2-16x+5 = 0 in (0,1)

6. 2x+ log10x =7 in (3.5,4) correct to 3 decimal places

3 Use Newton Raphson method to find the real root of the following equations:

1 Cos x = x

2 x3 + 5x + 3 = 0 in (1,2)

3 x2 + 4 sin x = 0 to 4 decimal places

4 x5-3.7 x4 +7.4 x3 – 10.8 x2 + 10.8x – 6.8= 0

4 (i) Find the value of 12 correct to 4 decimal places.

(ii) Obtain the value of 3 16 correct to 4 decimal places

5 Solve using Gauss- Elimination method: 1) 2x1+ 4x2 + x3 = 3. 2) 5x + y + z + u = 4 3x1 +2x2 –2x3 = -2. x + 7y + z + u = 12 x1 – x2 + x3 = 6. x + y + 6z + u = -5. x + y + z + 4u = -16.

6 Use Gauss - Jordan method to solve: 1) x+y+z=9, 2x-3y+4z=13, 3x+4y+5z=40

2) 10x-7y+3z+5u=6, -6x+8y-z-4u=5, 3x+y+4z+11u=2, 5x-9y-2z+4u = 7. 7 Use Gauss-Seidel method to solve:

1) 20x+y-2z=17, 3x+20y-z=-18, 2x-3y+20z=25 2) 4x+2y+z=14, x+5y-z=10, x+y+8z=20. starting with initial set (1, 1, 1) 3) 8x+y+z-u = 18, -2x+12y-z=-17, 2x+16z+2u = 54, y+2z-20u= -14

starting with ( 1, 1, 1 ). 8 Find the eigen values & the corresponding eigen vectors of the following

matrices:


31-21-32-

22-6 f)

2-0202-3001

e) 500620413

d)

0024-0321

c) 02-1-6-123-22-

b) 3424-76-

26-8 a)

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

9 Use Power method to find the dominant eigen value and the corresponding eigen vector for the following matrices:

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

21-01-21-

01-2 f)

24-20612-103415-

e) 221131122

d)

31-2132-22-6

c) 100121112

b) 34-24-76-

26-8 a)

Unit VI: Finite Differences and Interpolation

1 Write the difference table for the following set of values.

X: 1 2 3 4 5

y: 2 2.301 2.477 2.778 2.699

2 If f(x) is a cubic polynomial find the missing number.

X: 0 1 2 3 4

y: 5 1 -- 35 109

3 The values of ex for different x are tabulated below. Find the approximate values of e1.25

and e1.65.

x: 1.1 1.2 1.3 1.4 1.5 1.6 1.7

ex: 3.004 3.320 3.669 4.055 4.482 4.953 5.474

4 The table below gives the distance in nautical miles of the visible horizon for the given

heights, in feet, above the earth’s surface. Find d when x = 410 feet.

Height(x): 100 150 200 250 300 350 400

Distance(d): 10.63 13.03 15.04 16.81 18.42 19.90 21.27

5 Find the values of f(22) and f(42) from the following table:

x: 20 25 30 35 40 45

f(x): 354 332 291 260 231 204

6 Find f(x) when x = 0.1604 from the table given below :

X: 0.160 0.161 0.162


f(x): 0.15931821 0.16030535 0.16129134

7 Estimate the values of (i) sin 380 and (ii) sin 20 from the table given below:

x(degrees): 0 10 20 30 40

sin x: 0 0.17365 0.34202 0.50000 0.64279

8 Use Lagrange’s interpolation formula to find the value of y at x = 10 from the following

table:

x: 5 6 9 11

y: 12 13 14 16

9 Given log 654 = 2.8156, log 658 = 2.8182, log 659 = 2.8189, log 661 = 2.8202,

find log 656 using Lagrange’s interpolation formula.

10 Given the following table, find f(2.2) using Newton’s divided difference formula:

x: 1.0 2.0 2.5 3.5 4.0

f(x): 84.289 87.138 87.709 88.363 88.568

11 Apply Newton – Gregory forward difference formula to find f (5) given that

f (0) = 2, f (2) = 7, f (4)=10, f (6) = 14, f (8) = 19, f (10) = 24.

12 Find the polynomial approximating f (x) using Newton- Gregory forward difference

formula, given f (4) = 1, f (6) = 3, f (8) = 8, f(10) = 20.

13 Apply Newton- Gregory backward difference formula to find the polynomial approximating f (x),

given f (0) = 2, f(1) = 3, f (2) = 12, f (3) = 16.

14 Find f (7) Using Newton – Gregory backward difference formula given that

f (2) = 7, f (4) = 16, f (6) = 21, f (8) = 24, f (10) = 30, f (12) = 35.

15 Apply Newton’s divided difference formula to find f (8) given that

f (4 ) = 48, f ( 5 ) = 100, f ( 7 ) = 294, f ( 10 ) = 900, f ( 11 ) = 1210.

16 Solve f (x) = 0 using Lagrange’s interpolation formula given that

f (30) = -30, f ( 34 ) = -13, f ( 38 ) = 3, f ( 42 ) = 18.

17 Find the first and the second derivatives of the function at the given point , using the given formula: (a) Newton’s forward interpolation at x = 1.5 for x : 1.5 2.0 2.5 3.0 3.5 4.0 y : 3.375 7.0 13.625 24 38.875 59 (b) Newton’s backward interpolation at x = 1961 for Year : 1931 1941 1951 1961 1971 Population : 40.6 60.8 79.9 103.6 132.7

18 Use Trapezoidal rule to evaluate: 2 π/2 2 a) ∫ ex dx ;6 intervals b) ∫ sin2 x dx ; 6 intervals c) ∫ √ x dx ; 8 intervals 0 0 1

19 Use Simpson’s one-third rule to evaluate: 1 π/2 1 a)∫ dx ; 6 intervals b) ∫ e-x2 dx ; 6 intervals c)∫ sin x dx ; 6 intervals 0 √(1 + x3) -1 0

20 Use Simpson’s three – eighth rule: 1.5 5.2 1


a) ∫ x3 dx ; 6 intervals b) ∫ log x dx ; c) ∫ dx ; 6 intervals 1 ex – 1 4 0 1 + x2

21 Use Weddle’s rule to evaluate 6 1.4 3 a) ∫ dx b) ∫ log x dx c) ∫ dx 0 1 + x2 0.2 0 4x + 5

Unit VII: Calculus Of Variations:

1 Define variation of a function f(x,y,y’). Prove that the variation of a functional associated with f is equal to a functional associated with variation of f.

2 Derive Euler’s equations for a standard variation problem. 3 Discuss the particular cases of Euler’s equation, which reduce to Simple ordinary differential

equations. 4 Find the Extremum of the following functionals

a. dx )e2y (y'I1

0

x2∫ += y(0)=1,y(1)=0

b. dx sinx)-2y (y'I2

0

2∫=

π

y(0)=1,y((π/2 )=2

c. dxcoshx) 2(y'I1

0

2∫ += y y(0)=1,y(1 )=0

d. dx)12(y'I1

0

2∫ += xy y(0)=1,y(1 )=0

e. dx)2yey'(yIX2

X1

x22∫ ++=

f. dx -2ycos2x)y'-(yIX2

X1

22∫=

g. dxsinx)2y y'-(yIX2

X1

22∫ +=

h. ∫ ++= x2xy)d2yy'x(I 222

i. dx))y'x(1(y'IX2

X1

2∫ +=

j. dxy'xI

2

12

3

∫= y(1)=1,y(2 )=4

k. dx)y(y'I2π

0

22∫ −= y(0)=0, y( )=1

l. dx)y'(1y1I

X2

X1

2∫ +=


m. dx)yy'-1)(y'3xyI1

0

322∫ += under y(0)=0,y(1)=2

5 Prove that catenary is the plane curve which when rotated about a line generates a surface of

revolution of minimum area. 6 A uniform chain of fixed length is freely suspended from two points so as to hang at rest under

gravity. Determine the shape of the curve. 7 Show that the path in which a particle, in the absence of friction, will slide from one point to another

in the shortest time under gravity is a Cycloid. 8 Find the extremal of:

a. dxy'I1

0

2∫= under the conditions y(o)=0,y(1)=1 and subject to 1dxy1

0

2 =∫

b. )dxx(yI 21

0

2 += ∫ under the conditions y(o)=0,y(1)=0 and subject to

61dxy

1

0

2 =∫

c. ∫ −=π

0

22 )dxy(y'I under the condition y(o)=0,y((π/2)=1 and subject to

∫=π

0

ydxI

d. ∫=1

0

22 )dxy'-(xI under the conditions that y(o)=0,y( 1)=0 and ∫ ==1

0

2 2dx yI

9 Find the extremum of:

a. dt2y)x(yI1

0

22∫ ++= under the conditions x(0)=0 , y(0)=1,y(1)=3/2,x(1)=1.

b. dt)xy2y(2xy2π

0

222∫ −+− under the conditions x(0)=0, x((π/2)=1,

y(0)=1,y((π/2)=1.

c. dt)xy(2xy2π

0

22∫ ++ under the conditions x(0)=0 x((π/2)=1,y(0)=0,y((π/2)=1.

d. dt )x4y(xyT2

T1

22∫ ++ e. dt x.y)y(x2

1

t

t

22∫ ++

10 Find the extremum of:

a. ∫ +1

0

2 dx )y"(1 under the conditions y(0)=0,y(1)=1,y’(0)=1,y’(1)=1

b. ( )dx ''2

0

222∫ +−

π

xyy under the conditions y(0)=1,y(π/2)=0,y’((π/2)=1,y’(0)=0

c ( )∫ +−2

1

x

x

222 dx x'y'16y d ∫ +2

1

2 dx )''y'(2xyX

X


e ( )∫ +X2

X1

322 dx 2yx-y''y' under the conditions y(0)=y’(0)=y’’’(0)=0:y(1)=1 :

y’(1)=3,y’’(1)=6 11 Find the curve y=y(x) joining the points (0,0) and (1,0) for which the integral

dx'y'1

0

2∫ is minimum and y’(0)=1 ,y’(1)=2.

12 Find the geodesics on a plane 13 Show that arcs of great circles are geodesics on a sphere 14 Show that the circular Helix is a geodesic on a right circular cylinder. 15 Find the geodesics on a Right circular cone. 16 Find the Geodesics on a surface given that the arc length on the surface is

S= dx)y'x(1X2

X1

2∫ +

17 Find the Geodesics on the Helicoid x = u cosv ,y = usinv , z = kv given that

S= dududv)k(u1

U2

U1

222∫ ⎟

⎠⎞

⎜⎝⎛++

18 Find the Geodesics on the Catenoid of revolution x=u cosv, y= u sinv, z= f(u) given that

S= duv'uf'1U2

U1

222∫ ++ given by v=b+ duauxu

f'ax122

2

−+

Unit VIII: Difference equations and Z – Transforms

1 Define a difference equation with an example. Define the order of a difference equation with an example.

2 Form the difference equation corresponding to the family of curves y=ax+bx2. 3 From yn=a(2)n+b(-2)n, derive the difference equations by eliminating the constant. 4 Find the difference equation satisfied by

(i) y = (a/x)+b. (ii) y = ax2-bx.

5 Obtain the Z – Transform of the following: (i) an e-a/(n!) (ii) 1/(n+1)! (iii) (cos θ+isin θ)n (iv) an cosh nθ (v) e-an cos nθ

6 Show that (i) z (cosh nθ) = z (z - cosh θ)/(z2 - 2z cosh θ+1) (ii) z (sinh nθ) = (z sinh θ)/(z2 - 2z cosh θ+1)

7 If 4

2

)1(1452 U(z)

−++

=z

zz, evaluate u2 and u3.

8 Using the Z – Transform, solve (i) un+2+4 un+1+ 3un=3n with u0=0 and u1=1. (ii) yn+2-6yn+1+ 8yn=2n+6n.


06CSE32 : ELECTRONIC CIRCUITS

Faculty : No. of Hours: 52

% percentage of portions covered Class

#

Chapter title/ Reference literature

Topics to be covered Reference

Chapters Cumulativ

e 1 Clippers and limiters.

2 Clampers

3 Optoelectronics devices

4 Varactor diode

5 schottky diode

6

Unit #1 Diode Circuits

Special-purpose devices

#123-130,165-179.

Other diode

12 % 12 %

7 Base biased amplifier

8 Emitter biased amplifier

9 Small signal operation

10 AC Beta, AC resistance of the emitter diode

11 Two transistor models

12

Unit #2 Transistor AC

models #282-305

Analyzing an amplifier, AC Quantities on the data sheet

12 % 24 %

13 Voltage gain, loading effect of input impedance

14 Multistage Amplifiers Swamped Amplifier

15 Two Stage feedback, Troubleshooting

16 CC Amplifier , Out impedance

187 CE and CC Darling Connection

18 Voltage Regulator

19

Unit #3 Voltage amplifiers

CC & CB Amplifiers #314-339,380-389,393-

401,405-409. The Common-Base Amplifier

14 % 38 %

20 Amplifier Terms, Two Load Lines

21 Class A Operation, Class B Operation

22 Class B Push Pull Emitter Follower

23 Biasing Class B/AB Amplifiers

24 Class C Operation, Class A/AB Driver

25 Class C Formulas, Transistor Power rating

26

Unit #4 Power Amplifier

#342-377

Transistor Power rating

14 % 52 %

27 The Depletion MOSFETs, D-MOSFET Curves

28 Depletion-Mode MOSFET Amplifiers

29 Enchancement Mode- MOSFET.

30 The Ohmic Region

31 Digital Switching

32

Unit #5 MOSFET

#468-481

CMOS.

12 % 64 %

33 Frequency response Of an Amplfier ,Decible power gain.

34 Decibel Voltage Gain, Impedance Matching

35 Decibels above a Reference, bode plot

36 Four Type of Negative Feedback

37 VCVS Equations, The ICVS Amplifier

38 The VCIS Amplifier

39

Unit #6 Frequency Effect

#526-569 Negative Feedback

#663-690

Bandwidth.

13 % 77 %


% percentage of portions covered Class

#


Topics to be covered Reference

Chapters Cumulativ

e 40 Comparators with Zero Reference

41 Comparators with Nonzero Reference

42 Comparators with Hyteresis, Window Comparator

43 integrator,

44 Waveform waveform Conversion, Generation.

45 The 555 Timer, Astable Operation of the 555 Timer

46

Umit #7 Nonlinear Opamp-

amp Circuits

Oscillators #806-837,878-898

555 Circuits, The Phase –locked Loop, Function Generator ICs

12 % 89 %

47 Supply Characteristics, Shunt Regulators

48 Series Regulators, Monolithic Linear Regulators

49 Curremt Booster

50 DC to DC Converters

51 Switching Regulators

52

Unit #8 Regulated Power

supplies #908-947

Revision

11 % 100 %

Literature :

Publication Info Book Type Code Title And Author

Edition Publisher Year Text book

T1 Electronic Principles - by Albert Malvino and David J Bates

7th TMH 2007

Reference book

R1 Electronic Devices and Circuit Theory by Robert L Boylested and Louis Nashelsky

9th PHI/Pearson

2006

Reference book

R2 Electronic Devices and Circuit Theory by David A Bell 4th PHI 2006

Syllabus for test :

Test # Syllabus

T1 Class # 01 to 16

T2 Class # 17 to 34

T3 Class # 33 to 52


06CSE 33: LOGIC DESIGN

Faculty: No of Hours: 52

% of portions covered Class #


Topics to be covered Reference chapter

Cumulative

1 Overview of Basic Gates and Universal Logic Gates, AND-OR-Invert Gates

2 Positive & Negative Logic, Introduction to HDL 3 Boolean Laws and Theorems, Sum of-products Method 4 Truth Table to Karnaugh Map, Pairs, Quads, and Octets,

Karnaugh Simplifications 5 Don’t Care Conditions, Product-of-sums Method,

Product-of-sums Simplification 6 Simplification by Quine-MCcluskey Method 7

Hazards and Hazard Covers, HDL Implementation Models

13% 13%

8 Multiplexers, Demultiplexers, 1-of-16 Decoder 9 BCD-to-Decimal Decoders, Seven-segment Decoders 10 Encoders, EX -OR gates, Parity Generators and

Checkers 11 Magnitude Comparator, Read-only memory 12 Programmable Array Logic 13 Programmable Logic, Troubleshooting with a Logic

Probe 14

HDL Implementation of Data Processing Circuits

13% 26%

15 Binary Addition, Binary Subtraction, Unsigned Binary Numbers

16 Sign-Magnitude Numbers, 2’s Complement Representation

17 2’s Complement Arithmetic, Arithmetic Building Blocks 18 The Adder-Subtractor, Fast Adder 19 Arithmetic Logic Unit, Binary Multiplication and Division 20

Arithmetic Circuits using HDL

12% 38%

21 Clock Waveforms, TTL Clock, Schmitt Trigger 22 Monostables with Input Logic, Pulse-forming Circuits 23 RS Flip-flops, Gated Flip-flops, Edge-triggered RS 24 D,JK Flip-flops, Flip-flop timing, JK Master-slave Flip-

flops 25 Switch Contact Bounce Circuits, Various

Representations of Flip-flops 26 Analysis of Sequential Circuits 27

Conversion of Flip-flops – a synthesis example, HDL implementation of Flip-flop

13% 51%

28 Types of Registers, Serial In-Serial Out, Serial In-Parallel Out, Parallel In-Serial Out

29 Parallel In-Parallel Out, Applications of Shift Registers, Register Implementation in HDL

30 Asynchronous Counters, Decoding Gates 31 Synchronous Counters, Changing the Counter Modulus 32 Decade Counters, Presettable Counters 33 Counter Design as a Synthesis Problem 34

A Digital Clock, Counter Design Using HDL

13% 64%

35 Model Selection, State Transition Diagram, State Synthesis Table

36 Design Equations and Circuit Diagram 37

Implementation using Read Only Memory, Algorithmic State Machine

12% 76%


38 State Reduction Technique, Analysis of Asynchronous Sequential Circuit

39 Problems with Asynchronous Sequential Circuits

40 Design of Asynchronous Sequential Circuit 41 Variable, Resistor Networks, Binary Ladders 42 D/A Converters, D/A Accuracy and Resolution 43 A/D Converter-Simultaneous Conversion 44 A/D Converter-Counter Method, Continuous A/D

Conversion 45 A/D Techniques, Dual-Slope A/D Conversion 46

A/D Accuracy and Resolution

12% 88%

47 Switching Circuits, 7400 TTL, TTL Parameters 48 TTL Overview, Open-collector Gates 49 Three-state TTL Devices, External Drive for TTL Loads 50 TTL Driving External Loads 51 74C00 CMOS, CMOS Characteristics 52

TTL-to-CMOS Interface, CMOS-to TTL Interface

12% 100%

Literature

Publication information Book type Code Title & author

Edition Publisher Year

Text book T1 Digital Principles and Applications - by Donald P Leach, Albert Paul Malvino & Goutam Saha

6th TMH 2006

Reference book

R1 Fundamentals of Digital Logic with Verilog Design – by Stephen Brown, Zvonko Vranesic

2nd TMH 2006

Reference book

R2 Fundamentals of Logic Design - by Charles H. Roth

5th Thomson

2004

Reference book

R3 Digital Systems Principles and Applications - by Ronald J. Tocci, Neal S. Widmer, Gregory L. Moss

10th Pearson Education

2007

Syllabus for test Test Syllabus

T1 Class # 01 to 16

T2 Class # 17 to 34

T3 Class # 33 to 52

QUESTION BANK

BOOLEAN ALGEBRA AND COMBINATIONAL NETWORKS OBJECTIVE : This chapter gives you the details of

• Boolean algebra • Basic theorems and properties of Boolean algebra • Methods of simplifying Boolean functions • Implementation of basic gates using Universal gates • Normal Formulas and Canonical formulas

1. Define Binary operator. 2 2. List out different postulate used for algebraic structure. 2 3. Explain the commutative & Associative law 2 4. Discuss the following theorems with example

i) x+x=x ii) x.x=0 iii) x+1=1 iv) x.0=0 v) x+xy=x vi) x(x+y) =x


2 5. Explain Duality principle with an example. 2 6. Explain complement of function with an example. 2 7. Define truth table. 2 8. Why NAND & NOR gates are called universal gates. 2 9. Discuss canonical & standard forms of Boolean functions with an example. 4 10. Convert the following Boolean function to Sum of Minterms for F=A+B1C. 4 11. Convert the following Boolean function F=xy+x1z to product of Maxterm. 4 12. Bring out the difference between Canonical & Standard forms. 4 13. What are logical gates, mention different types of Logic gates. 4 14. Explain the operation of different Logic gates with neat diagram. 4 15. Minimize the following using K maps:

i)SOP expression given by f(A,B,C,D) = Σ m(0,1,2,3,5,9,14,15) + Σ Φ(4,8,11,12) ii)POS expression given by f(A,B,C,D) = ΠM(0,1,2,5,8,9,10) Implement the minimal expressions thus obtained using basic gates(both normal and inverted inputs can be used)

4*

16. List out the difference between combinational and sequential logic circuits 4* 17. Demonstrate by means of Truth table the validity of following theorem of Boolean algebra.

i) Associative law ii) DeMorgan's law for Validity iii) Distributive law 6

18. Simplify the following Boolean function to minimum no. of literals. i) xy+xy1 ii) (x+y) (x+y1) iii) xyz+x1y+xyz1 iv) y(wz1+wz)+xy v) (A+B)1 ((A1+B1)1

6

19. Reduce the Boolean Expression to required number of literal. i) BC+AC1+AB+BCD ii) [(CD1) + A ]1+A+CD+AB iii) [(A+C+D) (A+C+D1) (A+C1+D) (A+B1)

6

20. Obtain Truth table for function F=xy+xy1+y1z. 6 21. Convert the following to other canonical form.

i) F(x,y,z) =∑(1,3,7) ii) F(A,B,C,D)= ∑(0,2,6,11,13,14) iii) F(x,y,z) =Π(0,1,2,3,4,6,12)

6

22. Show that dual of Exclusive-OR is equal to its complement. 6 23. Expand the following function into canonical SOP form f(x1,x2,x3) = x1x3 + x2x3 + x1x2x3 6 24. Expand the following function into canonical POS form F(W,X,Q) =(Q+W1) (X+Q1) (W+X+Q)

W1+X1) 6

25. Mention different methods of simplifying Boolean functions. 6

26. Discuss K-map & Quine McCluskey methods for simplification of Boolean expressions. 6 27. Discuss K-map & Quine McCluskey methods. 6 28. Write advantages of K-map over Quine McCluskey method. 6 29. Define term Don’t care condition. 6 30. Explain K-map representation in detail & discuss the merits & demerits . 6* 31. Explain the tabulation procedure in detail & discuss merits & demerits. 6* 32. Compare K-map & Quine-Mcclusky methods for simplification of Boolean Expression. 6* 33. Obtain the simplified expression in sum of products for the following:

F(A,B,C,D,E) = ∑(0,1,4,5,16,17,21,25,29) BDE+B1C1D+CDE+A1B1CE+A1B1C+B1C1D1E1 F(x,y,z)= x1z + w1xy1+w(x1y+xy1)

6

34. Obtain simplified expression in SOP & POS form i) x1z1+y1z1+yz1+xyz ii) w1yz1+vw1z1+vw1x+v1wz+v1w1y1z1

and draw gate implementation using AND & OR gates

6

35. Given the function T(w,x,y,z)=Σ(1,3,4,5,7,8,9,11,14,15).Use K map to determine the set of all prime implicants. Indicate essential prime implicants, find three distinct mininmal expressions for T

10

36. Using tabulation method, determine the set of all prime implicants for the function f(w,x,y,z) = Σ(0,1,2,5,7,8,9,10,13,15) and hence obtain the minimal form of given function, employing decimal notation.

10*

37. Implement the following function with NAND and NOR gates. Use only four gates.Only normal inputs are available. F = W1 xz+W1yz+x1yz1+Wxy1z D = Wyz

10

38. Compare K-map & Quine-Mcclusky methods for simplification of Boolean Expression. Give their merits and demerits

10*

39. Using K-map simplify following Boolean expression & give implementation of same using i) NAND gates only

10


ii) AND,OR & Invert gates for F(A,B,C,D) =∑(2,4,8,16,31)+ ∑D(0,3,9,12,15,18) 40. Using K-map obtain Simplified expression in SOP & POS form of function

F(A,B,C,D)=(A1+B1+C1+D1) (A1+B1+C+D1) (A+B1+C+D1) (A+B+C+D1)(A+B+C+D) 10

41. Simplify Boolean function using don’t care condition for SOP & POS F=w1(x1y+x1y1+xyz)+x1z1(Y+w), d=w1x(y1z+yz1)+wyz F=ACE+A1CD1E1+A1C1DE, d= DE1+A1D1E+AD1E1

10

42. Simplify the following Boolean function using K-map method xy+x1y1z1+x1yz1 x1yz+xy1z+xyz+xyz1 F=A1C+A1B+AB1C+BC f (w,x,y,z)= ∑(0,1,2,4,5,6,8,9,12,13,14)

14

43. Simplify Boolean function by Tabulation method F(A,B,C,D,E,F,G)= ∑(20,28,52,60) F(A,B,C,D,E,F,G)= ∑(20,28,38,39,52,60,102,103,127)

14

44. Give two simplified irredundant expression for F(w,x,y,z)= ∑(0,4,5,7,8,9,13,15) 14* 45. Determine set of Prime implicants for function F(w,x,y,z)= ∑(0,1,2,5,7,8,9,10,13,15) 14* 46. Implement following function with NAND & NOR gates. use only four gates

F=w1xz+w1yz+x1yz1+wxy1z, d=wxy+wyz 14

47. The below circuit accepts BCD inputs for digits 0 to 9.the output is to be 1 only if input is odd. Design minimal logic circuit to accomplish this - A B BCD I/P C D

14

48. Minimize the following function with don’t care terms using Q.M. method f(A,B,C,D)= ∑m(5,7,11,12,27,29)+d(14,20,21,22,23) f(A,B,C,D)= ∑m(1,4,6,9,14,17,22,27,28,)+d(12,15,20,30,31)

14

49. Implement the following function using NAND gates f(X,Y,Z)= ∑(0,6) 14 50. Implement the following function using NOR gates F(x+y1) (x1+y)z1 14 51. Determine the set of Prime implicants for function F(w,x,y,z)= ∑(0,1,2,5,7,8,9,10,13,15) 14* 52. Using Quine-McCluskey obtain the set of Prime implicants for function

F(a,b,c,d,e)= ∑(4,12,13,14,16,19,22,24,25,26,29,30)+ ∑d(1,3,5,20,27) 14*

53. Find the minimal two level NOR realization for each following function f(A,B,C)= ∑m(1,4,6,8) f(A,B,C,D,E)= ∑m(3,5,7,12,23,27,28,30)

14

54. Find the minimal two level NAND realization for each following function f(A,B,C)= ∑m(0,2,3,7)

f(A,B,C,D,E)= ∑m(4,5,6,7,25,27,29,31)

14

Define literal. What are positive logic and negative logic? How positive logic can be converted to negative logic. Implement EXOR gate using minimum number of NAND gates. Write the truth table for each of the following logic functions: (a) F = V ⋅ W + X′ ⋅ Y′ ⋅ Z (b) F = (A′ + B′ + C ⋅ D) ⋅ (B + C′ + D′ ⋅ E′) (c) F = (W ⋅ X)′ ⋅ (Y′ + Z′)′ (d) F = (((A + B)′ + C′)′ + D)′ ( e) F = (A′ + B + C) ⋅ (A + B′ + D′) ⋅ (B + C′ + D′) ⋅ (A + B + C + D) Write the canonical sum and product for each of the following logic functions: (a) F = ΣX,Y(1,2) (b) F = ∏A,B(0,1,2) (c) F = ΣA,B,C(2,4,6,7) (d) F = ∏W,X,Y(0,1,3,4,5) (e) F = X + Y′ ⋅ Z

Logic Circuit

F(A,B,C,D


SIMPLIFICATION OF BOOLEAN EXPRESSIONS OBJECTIVE: This chapter deals with Definition and design of combinational logic circuit like adders, subtractors and code converters Implementation of logic circuits with only NAND and NOR gates How errors can be detected & corrected while transferring as well as receiving data. 55. Define combinational circuit with block diagram, Explain the elements of combinational circuit. 4 56. Discuss the full adder with an example. 4 57. Discuss the Half adder with an example. 4 58. Discuss enable control inputs. 4 59. Explain the code conversion procedure. 4 60. Given 3x8 decoder, show the construction of 4x16 decoder. 6 61. Explain grouping and simplification process in K maps using the 3 variable and 4 variable maps. 6* 62. Define parity generator and parity checker. 6 63. Give the main steps for designing combinational circuits. 6 64. Mention the limitations of designing logic circuit in practical design method. 6 65. Define full adder & half adder, explain the working of it with an example. 6 66. Mention the difference between full and half adder. 6 67. Explain code conversion, give Boolean function for converting BCD TO EXCESS-3 converter. Give

the logic diagram for the same. 6

68. Discuss about the analysis procedure for designing logic circuit. 6 69. Mention the steps to obtain output Boolean function, truth table from the logic diagram. 6 70. Discuss block diagram method with an example. 6 71. Give the block diagram procedure for implementing Boolean function with NOR & NAND gates. 6 72. Discuss odd & even parity generation, checking with an example. 6 73. Give the logic diagram for 3-bit odd parity generator & checking. 6 74. Design BCD to 7 segment decoder using NAND gates only 6 75. Implement the full subtractor with two half adder and OR gate 8 76. Design a combinational circuit that converts decimal digit from 8,4,-2,-1 code to BCD 8 77. Design a combinational circuit that converts decimal digit from 2,4,2,1 code to 8,4,-2,-1 code 8 78. Obtain NAND logic diagram of full adder from Boolean function.

C = xy+xz+yz S = c (x+y+z)+xyz

8

79. Show that a) AΟB0C0D=∑(0,3,5,6,9,10,12,15) b) A⊕ B⊕ C⊕ D=∑(1,2,4,7,8,11,13,14) c) A⊕ B⊕ C= AOBOC d) A⊕ BOC= AO B⊕ C.

8

80. Implement the given Boolean function using NAND gate (A+B1)(CD+E). 8 81. Implement the given Boolean function using NOR gate A(B+CD)+BC1 8 82. Design combinational circuit to check for even parity of four bits. A logic 1 output is required when

four bits do not constitute an even parity. 8

83. Implement the Boolean function F= AB1CD1+A1BCD1+AB1C1D+A1BC1D with EXCLUSIVE –OR & AND gates

8

84. Design a combinational logic circuit whose input is a 4 bit binary number and output is the 2’s complement of input number. Implement by using suitable gates.

8*

85. Show that A O B O C O D = ∑ ( 0,3,5,6,9,10,12,15) 6* 86. Design a combinational circuit that converts 4-bit reflected code number to a four bit binary

number, implement the circuit with EX-OR gates. 10

87. Using truth table and k map simplification design a BCD to EXCESS -3 code converter. Implement the code converter using BASIC GATES ( only normal inputs can be used)

10*

88.

Using decoder implement the following Logic functions. Active High decoder with OR gate. Active Low decoder with NAND gate. Active High decoder with NOR gate. Active Low decoder with AND gate.

12

89. Design 2-4 decoder with enable input E. 10

90. Design 3-8 decoder 10

91. Design 4-16 decoder 10 92. . Mention the application of decoder. 10 93. Design a code converter that converts 4-bit number from Grey code to binary code. 10


94. Design 2-bit adder circuit using two level NAND gate circuit for each output. the inputs are 2- bit binary number’s a1a0 & b1b0,the output’s are the 2-bit binary sum s1s0 & carry output c1 only.

10

95. Using only half adder, draw a circuit that will add 3-bits xiyizi together,producing carry & sum bits Si,cI as shown in following table. Xi yi zi ci si 0 0 0 0 0 0 0 1 0 1 0 1 0 0 1 0 1 1 1 0 1 0 0 0 1 1 0 1 1 0 1 1 0 1 0 1 1 1 1 1

10

96. Give the truth table for half adder and full adder, develop the simplified expression for sum & carry of a full adder & realize the full adder using only half adder

10*

97. Design a EXCESS-3 code to BCD code using NAND gates only. 10* 98. List the PLA table for the BCD to excess – 3 code converter. 6* 99. Design BCD to 8,4,-2,-1 code converter by using K-map method and implement the circuit by

using AND-OR-INVERT gates only. 10*

100. Design a full adder & full subtractor ,give their truth table, simplified expression and circuit diagrams

20*

101. What is decoder? what are its advantages? Design a decimal decoder which converts information from BCD to DECIMAL.

20*

How a decoder can work as a demultiplexer LOGIC LEVELS AND FAMILIES OBJECTIVE: This chapter gives you the details of TTL: Different Types and Logic MOSFET and Types NMOS and CMOS Comparison of above logic families 102. Define Fan-in, Fan-out 4 103. Describe TTL family 6 104. Explain NMOS types, and NMOS gates with their advantages and disadvantages 10 105. Compare the logic families a). TTL b). NMOS c). CMOS 8 106. With the aid of a neat circuit diagram explain the operation of a 2 input TTL nand gate with Totem

output. 8*

Define noise margin

107. Define combinational circuit with block diagram, Explain the elements of combinational circuit. 10 108. Discuss the full adder with an example. 10 109. Discuss the Half adder with an example. 8

LOGIC DESIGN WITH MSI COMPONENTS AND PROGRAMMABLE LOGIC DEVICES OBJECTIVE: This Chapter gives you the details of Binary adders and subtractors Carry Lookahead Adders and Comparators Encoders and Decoders Multiplexers and Demultiplexers PLDs , PLAs and PROMs


110. Discuss enable control inputs. 6 111. Explain the code conversion procedure. 6 112. Given 3x8 decoder, show the construction of 4x16 decoder. 10 113. Define parity generator and parity checker. 8 114. Give the main steps for designing combinational circuits. 10 115. Mention the limitations of designing logic circuit in practical design method. 8 116. Define full adder & half adder, explain the working of it with an example. 14 117. Mention the difference between full and half adder. 8 118. Explain code conversion, give Boolean function for converting BCD TO EXCESS-3 converter. Give

the logic diagram for the same. 12

119. Discuss about the analysis procedure for designing logic circuit. 10 120. Mention the steps to obtain output Boolean function, truth table from the logic diagram. 10 121. Discuss block diagram method with an example. 12 122. Give the block diagram procedure for implementing Boolean function with NOR & NAND gates. 12 123. Discuss odd & even parity generation, checking with an example. 10 124. Give the logic diagram for 3-bit odd parity generator & checking. 10 125. Design BCD to 7 segment decoder using NAND gates only 14 126. Implement the full subtractor with two half adder and OR gate 12 127. Design a combinational circuit that converts decimal digit from 8,4,-2,-1 code to BCD 12 128. Design a combinational circuit that converts decimal digit from 2,4,2,1 code to 8,4,-2,-1 code 12 129. Obtain NAND logic diagram of full adder from Boolean function.

C = xy+xz+yz S = c (x+y+z)+xyz

12

130. Show that a) AΟB0C0D=∑(0,3,5,6,9,10,12,15) b) A⊕ B⊕ C⊕ D=∑(1,2,4,7,8,11,13,14) c) A⊕ B⊕ C= AOBOC d) A⊕ BOC= AO B⊕ C.

14

131. Implement the given Boolean function using NAND gate (A+B1)(CD+E). 10 132. Implement the given Boolean function using NOR gate A(B+CD)+BC1 10 133. Design combinational circuit to check for even parity of four bits. A logic 1 output is required when

four bits do not constitute an even parity. 12

134. Implement the Boolean function F= AB1CD1+A1BCD1+AB1C1D+A1BC1D with EXCLUSIVE –OR & AND gates

12

135. Design a combinational circuit that converts 4-bit reflected code number to a four bit binary number, implement the circuit with EX-OR gates.

12

136. Using decoder implement the following Logic functions. Active High decoder with OR gate. Active Low decoder with NAND gate. Active High decoder with NOR gate. Active Low decoder with AND gate.

14

137. Design 2-4 decoder with enable input E. 10 138. Design 3-8 decoder 8 139. Design 4-16 decoder 8 140. Mention the application of decoder. 6 141. Design a code converter that converts 4-bit number from Grey code to binarycode. 8 142. Design 2-bit adder circuit using two level NAND gate circuit for each output. the inputs are

2- bit binary number’s a1a0 & b1b0,the output’s are the 2-bit binary sum s1s0 & carry output c1 only.

12

143. Describe PLAs in detail using only half adder, draw a circuit that will add 3-bits xiyizi together, producing carry & sum bits Si, cI as shown in following table. Xi yi zi ci si 0 0 0 0 0 0 0 1 0 1 0 1 0 0 1 0 1 1 1 0

14


1 0 0 0 1 1 0 1 1 0 1 1 0 1 0 1 1 1 1 1

144. Implement in FULL ADDER circuit using a 3:8 decoder and two OR gates 10* 145. Using truth table and k map simplification show implementation of a FULL ADDER is SOP 10*

146. Implement the Boolean function: F(A,B,C,D)= ∑m(0,1,2,3,4,8,9,14,15) using an 8:1 MUX.

10*

147. Explain the principle of operation in EPROM and EEPROM. 10* 148. Explain the principle of operation in SRAM and DRAM 10*

FLIP – FLOPS AND SIMPLE FLIP – FLOP APPLICATIONS

OBJECTIVE: This chapter gives you the Details of Latches: SR and D Latches Master-slave( JK) flip-flops Registers and Counters , Different Types

149. Mention the difference between combinational & sequential circuits with block diagram 4 150. Mention the difference between asynchronous & synchronous circuits with example. 4 151. Difference between Latch & Flip flop give example 4 152. Define clocked sequential circuit. 4 153. Difference between Characteristic & Excitation table. 4 154. Explain the operation of SR flip flop 5* 155. What is Race round condition. Explain 5 156. Explain the operation of JK flip-flop. With logic diagram, characteristic table. 5 157. Discuss how unstable condition S=R=1 is avoided in storage latch of the following

a) D latch b) JK flip flop c) T flip flop 5

158. Explain clocked RS flip flop with logic diagram 5 159. Show that clocked D flip-flop can be reduced by one gate 5 160. Explain how D & T flip flop works with logic diagram 5 161. Discuss state table, state diagram, and state equation with example. 5 162. Explain registers. 8 163. Give a block diagram of sequential circuit employing register as a part of sequential circuit. 8 164. Discuss shift registers. 8 165. Discuss serial transfer of information from one register to other. 8 166. Mention the capabilities of shift register 8 167. Explain universal shift register(74194) 8 168. Design synchronous BCD counter using JK flip flops. 8 169. Explain the operation of one shot Monostable multivibrator 8 170. Explain how shift register can be used as counters. 8 171. Mention the difference between ripple & synchronous counters. 8 172. Explain the operation of Master slave JK flip flop with circuit diagram. Give benefits of it. 10* 173. Explain state reduction & assignment by taking an example. 10 174. Discuss about flip flop excitation table write excitation table for SR,JK flip flops 10 175. Discuss the procedure for designing sequential circuits. 10 176. Discuss the procedure for designing sequential circuits. 10 177. Define counter, & write state diagram for 3-bit binary counter. 10 178. Define counter, & write state diagram for 3-bit binary counter. 10 179. Design sequential circuit with JK flips flops to satisfy the following state equations.

A(t+1)= A1B1CD+A1B1C+ACD+AC1D1 B(t+1)=A1C+CD1+A1BC1 C(t+1)=B, D(t+1)=D1

10

180. Design the binary counters having following repeated binary sequence. use IC flip flops Only .0,4,2,1,6.

10*

181. Clearly distinguish between synchronous & asynchronous circuits, Combinational & sequential ckts, Latch & flip-flop

10*

182. Design BCD counter with JK flip flops 10


183. Design a counter with following binary sequence a) 0,1,2 b) 0,1,2,3,4 c) 0,1,2,3,4,5,6

10

184. Discuss why condition S=R=1 leads to unstable condition for SR latch construct state diagram for following table, what is the logic equation for output variable Z. 0 1 A D/1 B/0 B D/1 C/0 C D/1 A/0 D B/1 C/0 Examine 7476 Jk flip flop, discuss why PRE1 & CLR1 inputs are refereed to as asynchronous inputs. While JK are called synchronous inputs.

10

185. Give logic diagram of 4 bit bi-directional shift register with parallel capability & briefly explain I it’s operation.

10*

186. Give logic diagram of 4-bit binary ripple counter & BCD Ripple counter 10 187. Give logic diagram of ring counter & Johnson counter 10 188. Discuss binary up/down counters 10 189. Construct mod 6 counter using MSI chip. 10 190. Construct Mod 12 counter using MSI chip. 10 191. Design a serial adder using sequential logic procedure 10 192. Explain bi-directional shift register with parallel load 10 193. Discuss asynchronous up/down counter & explain presettable counter 10 194. Explain schmitt trigger 10 195. Design mod-3 counter using J-K flip-flops sketch waveforms for outputs when clock is Applied &

verify its operations. *20

196. Discuss MAR,MBR, Memory register addressed by MAR. 5 197. Explain all operations in a DRAM cell 5* 198. Explain SRAM and DRAM 5* 199. Explain read only memory with block diagram 5 200. Explain the working of Johnson counter with MSI chip. 5 201. List the PLA table for BCD to Excess-3 code converter 10* 202. Discuss the PLA table, Write the PLA table for the following truth table

A B C F1 F2 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 1 1 0 1 1 0 0 1 0 1 0 1 1 1 1 1 0 0 0 1 1 1 1 1

10

203. Design mod – 5 synchronous binary counter having the following repeated binary sequence using J – K flip flops. 0,4,2,1,6,0,4…..

10*

204. Write the logic diagram of a 4 bit bi-directional shift register with parallel load capability and explain its operations

10*

205. Explain Johnson counter with its circuit diagram , timing diagram and statue diagram. 10* 206. Design a MOD12 asynchronous (ripple) up counter using JK flip flops. Explain the operation briefly

using timing diagram 10*

207. Using logic circuit , truth table and timing diagram explain the operation of a JK Flip flop .Show excitation table and the characteristics equation .

10*

208. Design a counter that has a repeated sequence of SIX states shown in the state diagram. Use JK flip flops

10*

209. With timing diagram and transition table, explain the operation of 14 bit SISO shift register using D 10*

0 1 2 4 5 6


flip flop 210. Write short notes on:

a)JK master slave flip flop b)synchronous counter c)ring counter d)monostable multivibrator e)PROM Define metastablity. Build T flip flop from JK flip flop.

10*

SYNCHRONOUS SEQUENTIAL NETWORKS OBJECTIVE: This chapter gives you the idea of Clocked Synchronous Sequential Networks : Structure and Operation Excitation and Output Expressions Transition Equations and Tables, State diagrams Network Terminal Behavior 211. Explain the structure and operation of Clocked synchronous sequential netwoks 10 212. What are uses of Transition tables and Excitation tables 10 213. Write a note on Network terminal behavior 5

Marks No. of Questions 2 8 4 19 5 14 6 41 8 29 10 69 12 12 14 18 20 3

Total 213


06CSE 34: DISCRETE MATHEMATICAL STRUCTURES

Faculty: No of Hours: 52

% of portions covered Class #


Topics to be covered Reference chapter

Cumulative

Set Theory Sets and Subsets 1 2 Set Operations and the Laws of Set Theory 3 Counting and Venn Diagrams 4 Countable and Uncountable Sets 5

Chapter #1,3 Set Theory T1: page #127 – 157 Counting T1: page 3 - 6

A word on Probability

10% 10%

Mathematical Induction and Recursive Definitions 6 7 Fundamentals Of Logic Basic connectives 8 Truth Tables 9

Chapter #2 Fundamentals of Logic T1:page#47-157

Tautologies 8% 18%

Logical equivalence 10 11-12 The laws of logic

13 Logical implications 14-15 Rules of Inference 16 Quantifies: Definition, The use of Quantifies,

17-18 Proofs of Theorems 19 Relations : Cartesian Products and Relations

20-21 Properties of relations 22-23 Computer recognition: Zero – one matrices and

directed graphs 24-25

Chapter#5 Relations T1:page#217-218,311-319

Equivalence Relations and Partitions

30 % 48%

Partial Orders- Poset 26 27 Hasse Diagram 28 Linearly ordered set

29-30 Extremal elements of a Poset, Lattices 31-32 Functions- Plain, One-to-One, Onto and Bijective

Functions 33 Functions in Computer Science 34 Permutation Function and Hashing function

35-36 Function Composition and Inverse Function GROUPS AND CODING THEORY

37 Binary operations and properties 38-39 Definition of a Group, Examples, Elementary Properties

40-41

Chapter #5,6 Functions T1:page# 222-249 Groups and coding theory T1: page 300- 318

Homomorphisms, Isomorphisms and Cyclic Groups

30% 78%

Cosets and Lagrange’s Theorem 42 43 Elements of Coding Theory 44 The Hamming Metric 45 The Parity-Check and Generator Matrices 46 Groups Codes- Decoding with Coset Leaders 47 Hamming Matrices 48 Ring Structure-Definition and examples

49-50 Ring Properties and Substructures 51-52

Chapter#7 Groups , SEMIGROUPS Ring Structures , T1:Page#319-351

Revision

22% 100%


Literature:

Publication info Book Type Code Title & Author

Edition Publisher Year

Text Book T1 Discrete and Combinatorial Mathematics by Ralph P. Grimaldi

4th Pearson Education

2002

Reference Book

T2 Discrete Mathematical structures for compute science by Kolman, Robert C. Busby and Sharon Ross

2nd PHI publications

1999

Reference Book

R1 Discrete Mathematical Stuctures with Applications to computer Science by J.P Tremblay & R. Manohar

- Tata-Mcgraw, Hill,

1987

Reference Book

R2 Discrete Mathematics and its Applications by Kenneth H. Rosen

5th Tata-McGraw Hill

2003

Syllabus for test :

Test # Syllabus

T1 Class # 01 to 12

T2 Class # 13 to 25

T3 Class # 26 to 52

SET THEORY OBJECTIVE: Every study on mathematical sciences begins with set theory. The study of discrete mathematical structures is no exception. An elementary and informal exposition of set theory is presented from the point of discrete mathematics. 1. Define the following with an example.(i)Subset (ii) Equal sets (iii) Power set of a set . 4* 2. Prove that the null set is a subset of every set. 2 3. Show that the null set is unique. 2 4. List all the subsets of {1, ϕ, { ϕ}} 2 5. Prove that symmetric difference is commutative. 2 6. Prove that symmetric difference is associative. 2 Let A,B,C be arbitrary sets. 7. Show that (A-B)-C = A -(B U C) 2 8. Show that (A-B)-C = (A -C)-(B-C) 2 9. Show that (A U B ) - ( A ∩ B ) = (A - B) U (B - A) (*) 2 10. A is a set of material numbers that have RECEIPT-RECORDS. B is a set of material numbers that have

ISSUE RECORDS.

A = {1,2,4,7,10,13,17,17,21,25,30} B = {1,3,4,5,9,11,12,13,15,19,25} Write down the set of i. material numbers that have any one type of record. 2 ii. material numbers that have both types of records. 2 iii. material numbers that have RECEIPT-RECORDS but no ISSUE-RECORDS 2 iv. material numbers that have ISSUE-RECORDS but no RECEIPTS RECORDS and 2 v. material numbers that have either of the records but not both. 2

11. Illustrate with an example that RELATIVE COMPLEMENT is not COMMUTATIVE or ASSOCIATIVE operation. 4 12. A firm manufactures 50 cars daily. 10 of them are fitted with RADIO-RECEIVERS, 15 with AIR-

CONDITIONERS and 23 with T.V. SETS. 6 of them are fitted with both RADIOS & T.V. SETS and 10 of them with T.V.SETS and AIR-CONDITIONERS. 7 of them with Radios and AIR-CONDITIONERS, 4 of them with all the three. Find the number of cars that are not fitted with any of the above.

4

13. Let A, B and C be finite sets. Show that * i) |A ∪ B ∪ C| = |A| +|B| +|C| - |A ∩ B| - |B ∩ C| - |C ∩ A| + |A ∩ B ∩ C|

4

14. If one tosses a fair coin four times, what is the probability of getting two heads and two tails? 4 15. How many permutations of the digits 0,1,2,3…,9 either start with a 3 or end with a 7 or both? 4


16. If the letters in the acronym WYSIWYG are arranged in a random manner, what is the probability that arrangement starts and ends with the same letter?

4

17. Prove by mathematical induction : w Σ i 2 = w (w+1) (2w+1) i=1 6

5

18. Show the following by induction 5 19. n ! > 2 n for n ≥ 4 5 20. 1.2 + 2.3 + ... + n (n+1) = n (n+1)(n+2) / 3 5 21. Show that n 3 + 2 n is divisible by 3. 5 22. Show, by induction any integer composed of 3n identical digits is divisible by 3n. 5

23. Using mathematical induction show that 1 3 + 2 3 + ... + n 3 = [ n(n+1) ]2 2

5

24. Prove by mathematical induction that 3 / (n3 – n) for every positive integer n . 5 25. Prove by mathematical induction that 12 + 32 + 52 + . . . .+(2n - 1)2 = (n(2n+1)(2n-1) / 3) 5 26. Give a recursive definition for each of the following integer sequences c1,c2,,…….where for all n∈Z+ .a) cn

= 7n b) cn=3n +7 c) cn= 7n d) cn = n2 e) cn= 2-(-1)n

5

FUNDAMENTALS OF LOGIC

OBJECTIVE: Logic is the science dealing with the methods of reasoning. Reasoning plays a very important role in every area of knowledge particularly mathematics.

27 Define with an example (i) statement (ii) statement formula (iii) well defined formula (iv) connective (v) tautology (vi) contingency (vii) contradiction

1 each

28

Construct the truth tables and show the truth values of the following formulae (*) 1) (P∧(P→Q)) → Q 2) (P→ Q) ↔ ( ⎤ P∨R) 3) (⎤ P∧ (⎤ Q∧ R)) ∨ (Q ∧ R) ∨ (P ∧ R) ⇔ R 4) (P∨ Q) ∧ (P → R) ∧ (Q → R) ⇒ ⎤R 5) (P⇒ Q) ⇔ (⎤ Q⇒ ⎤ P) 6) (P∧R) → S ⇔ P → (R → S) 7) (⎤ (P∧Q) → ( ⎤ P∨ (⎤P ∨ Q))) ⇔ ( ⎤P ∨ Q)

2 each

29 Define with an example principal conjunctive and principal disjunctive normal forms of a given formula. 4

30

Obtain the above for the following : 1. P ∨ (⎤ P → (Q ∨ (⎤Q → R))) 2. P → ((P → Q) ∧⎤ (⎤Q∨⎤P)

3.(⎤P → R) ∧ (Q →P)

4. (⎤P ∨ ⎤Q) → (P → ⎤Q) 5.(P ∧ Q) ∨ ( ⎤P ∧ R) ∨ (Q ∧ R) 6. (P → (Q ∧ R)) (⎤P → (⎤Q ∧ ⎤R)

2 each

31

Without constructing the truth table, prove the following : (ii) 7P logically follows from S→ 7Q, SVR, R→ 7Q and P→ Q (iii) The premises P→ Q , Q→ S, R →7S and P^R are inconsistent (iv) SVR is tautologically implied by (PVQ) ^ (P → R) ^ (Q→ S) (V) R → S can be derived from the premises P→ (Q → S), 7RVP and Q (vi) 7 (P^Q) follows from (7PV7Q)

2 each

32 Define with an example : (i) Predicate (ii) free and bound variables (iii) Existential and universal quantifiers (iv) Scope of the quantifier (v) Universe of discourse

2 each

33 Illustrate with examples, the principles of (i) Existential generalization & specification (ii) Universal generalization & specification

4 each

34

Using the inference theory of predicate calculus , show that 1. (x) (P (x) → Q(x)) ∧ (x) (Q(x) → R (x))⇒ (x) (P(x) → R(x)) 2. (x) (H (x) → M (x)) ∧ (∃x) H (x) ⇒ (∃x) M(x) 3. (x) (P(x)∨ Q(x)) ⇒ (x) P (x) ∨ (∃x) Q(x) Use indirect method of proof 4.(∃x) (P(x) ∧ Q(x)) ⇒ (∃x) P(x) ∧ (∃x) Q(x) 5.(x)(P(x) → Q(x)), (x) R(x) → ⎤ Q(x) ⇒ (x) R(x) → ⎤P(x) 6.(x) A(x) ∨ (x) B(x) ⇒ (x) A(x) ∨ (x) B(x)

4 each


RELATIONS OBJECTIVE: Relationships between people, number, sets and many other entities can be formalized in the idea of a binary relation. The concept of binary relation gives several geometric and algebraic methods of representing such objects. Function is a special type of relation that plays an important role in mathematics, computer science and many applications. The notion of partially ordered sets including lattices and Boolean algebra is useful in set theory, algebra, sorting and searching especially in the case of Boolean algebra in the construction of logical representations for computer circuits. 35 Show that : 4

(a) A X (B ∩ C) = ( A X B) ∩ ( A X C) each (b) (A ∩ B) X(C ∩ D) = ( A X C) ∩ (B X D)

36 Show by means of an example that A X B ≠ B X A and ( A X B ) X C ≠ A X ( B X C )* 4 37 List all partitions of A= {a, b,c,d } 4 38 Show that if a relation on a set is transitive and irreflexive then it is asymmetric. 4 39 Define an equivalence relation. Give an example 2 40 Let A = ( 1,2,3) x ( 1,2,3,4) . Define the following equivalence relation R on

A: (x,y), (u,v) ∈ R iff x + y = u + v. Compute the partition of A induced by the equivalence relation R.

4

41 If R is a reflexive relation on a set A, prove that R2 is also reflexive on A. 4 42 Let A = {1,2,3} & R be a partial order (is a subset of) defined on the power set of A. Represent R in a

Hasse diagram. 4

43 Write down the set of positive integers that divide 40. Write a relation of divisibility on the above set. Check whether it is a partial order relation. If so, draw the Hasse diagram representing it.

6

44 Give a relation which is both a partial ordering relation & an equivalence relation . 4 45 Let A be a given finite set and p(A) its power set. Let ⊆ be the inclusion relation on the elements of

p(A). Draw the Hasse diagram of < p(A), ⊆ > for i. A = {a,b} ii. A = {a,b,c} 8

46 Define the terms i .GLB ii. LUB iii. DUAL. 1 each

47 Let A be the set of factors of a particular positive integer m and let <= be the relation divides, i.e., R = { (x,y) / x ∈ A & y ∈ A & (x divides y)}. Draw the Hasse diagrams for i. m = 6 ii. m = 45

4 each

48 Show that in a lattice, if a ≤ b ≤ c, then (a * b) & (b * c) = b = ( a & b) * (a & c) and a ≤ a join b. 4 49 Let a,b,c be elements in a lattice (A, ≤). Show that, if a ≤ b then a join (b meet c ) ≤ b meet ( a join c) 4 50 What is a distributive lattice? Prove that in a given distributive lattice, an element has a unique

complement. 6

FUNCTIONS OBJECTIVE: Function is a special type of relation that plays an important role in mathematics, computer science and many applications. The notion of partially ordered sets including lattices and Boolean algebra is useful in set theory, algebra, sorting and searching especially in the case of Boolean algebra in the construction of logical representations for computer circuits. 51 Define an injective function with an example. 2 52 Define a surjective function with an example. 2 53 For each of the following functions f:Z→Z, determine whether the function is one-to-one and whether it is

onto.If the function is not onto, determine the range of f. i)f(x)= x+7 ii)f(x)=2x-3 iii)f(x)=-x+5 iv)f(x)=x2 v) f(x)= x2 +x

2

54 Define a unary operations on a Set A with an example. 2 55 Define a Commutative and associative binary operations on a Set A with example. 4 56 Let f: AX A →B be a binary operation. If f has an identity, show that it is unique 4 57 Define a 1-1 correspondence with an example. 2 58 Define composite function with an example. 2 59 Let f: R →R, g : R →R,be defined by f(x)=x2,g(x)=x+5.Find ( )fg ο (x) and ( )gf ο (x) 4

60 Define the converse of a relation R with an example 4 61 Prove that a function f is invertible iff it is 1-1 and onto 4 62 For each of the following functions f: R →R, determine whether f is invertible and if so determine f-1

(a) f= {(x,y)|2x+3y=7} (b) f= {(x,y)|ax+by=c, b ≠ 0} (c) f= {(x,y)|y=x3} (c) f= {(x,y)|y=x4+x}

4 each

63 Define a permutation of set A with an example. 2 64 Let A = {1,2,3,4,5,6} compute (4,1,3,5) ο (5,6,3) and (5,6,3) ο (4,1,3,5) 6 65

Let A be finite set with n elements , n ≥2. Show that there are 2!n even permutations and

2!n odd

permutations

6


66 Define the characteristic function with an example. Prove that BABA fff =∩ and

BABABA fffff −+=∪

5

GROUPS AND CODING THEORY OBJECTIVE: Groups are simple mathematical structures the study of which is essential in the field of computer scienceCoding theory has developed techniques for introducing redundant information in transmitted data that help in detecting and sometimes in correcting errors. Some of these techniques make use of group theory. 67 Define with examples: a. Group b. Abelian and cyclic group c. Subgroup 2 68 If H is a non empty subset of a group G, Show that H is sub group of G iff (a)for all a,b ∈H,ab∈H

and (b) for all a ∈ H, a-1 ∈ H. 4

69 Define the binary operation ο on Z by x ο y = x+y+1. Verify that (Z, ο) ia an abelian group. 4 70 For any group G prove that G is abelian iff (ab)2 = a2 b2 for all a, b ∈ G 4 71 Does the set of all integers under multiplication form an abelian group? Explain your answers. 4 72 Define group homomorphism and isomorphism with an example. 6 73 Let a ∈ G with o (a) = n. If k ∈ Z and ak = e, show that n /k. 4 74 Let f: G → H be a group homomorphism on to H. If G is abelian prove that H is abelian. 4 75 If G is a finite group and a ∈ G. Shoe that order of a divides order of G. 4 76 Define the term Hamming metric. 4 77 For the following encoding function, find the minimum distance between the code words. Discuss the error

detecting and error correcting capabilities of it.

E: 52

22 ZZ ⎯→⎯ ,

00 → 00001 01→ 01010 10 → 10100 11→ 11111

6

78 In a group code prove that the minimum distance between distinct code words is the minimum of the weights of the nonzero elements of the code.

5

79

Let

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡=

100111001011010011011

H be the parity – check matrix for a Hamming (7, 4) code.

a) Encode the following messages : 1000 1100 1011 1110 1001 1111. b) Decode the following received words : 1100001 1110111 0010001

5 each

80 Define a ring with an example. 2 81 Define an integral domain and a field with example. 4 82 Define addition and multiplication denoted by ⊕ and respectively on the set Q as follows. For a, b ∈ Q, a

⊕ b = a +b +7, a b = a+b+(ab/7). a) Prove that (Q, ⊕ , ) is a ring.

b) Is this ring commutative? c) Does the ring have a unity? d) Is this ring an integral domain?, a field?

2

83 For a ring (R, +, .), prove that a) If R has a unity then it is unique. b) If R has a unity and x is a unit of R then the multiplicative inverse of x is unique.

4

84 Show that the relation congruence modulo n is an equivalence relation on Z. 4

Marks No. of Questions 1 2 2 28 4 34 5 12 6 8

Total 84


06CSE35 : DATA STRUCTURES WITH C Faculty : No of Hours:52

% of Portions covered Class

# Chapter Title/Reference

Literature Topic to be covered Reference

Chapter Cumulative

1. Pointers: Concepts, pointer variables. 2. Accessing variables through pointers. 3. Pointer declarations and their usage 4. Pointers and functions, pointers to pointers

compatibility 5. Lvalue and Rvalue,Arrays and pointers, pointer

arithmetic. 6. Understanding complex declarations 7. Malloc, calloc, free and realloc functions 8.

Unit I 1.C Language Features

Pointers, Dynamic memory allocation,

T1:Page # 426-448,471-492

Array of pointer

19% 19%

9. String concepts C strings, String I/O function. 10.

Unit II 2.Strings

T1:Page #519-557 Array of strings, String manipulation function, Memory formatting.

15% 34%

11. Enumerated structure, and union 12. The type definition, Enumerated

types,structure,Accessing structures 13.

3.Derived types T1:Page #588-623

Complex structures, Array of structures, Structures and functions,Unoins

7% 41%

14. Classification of files, Using Binary Files 15.

4.Binary Files: T1:Page #655-671 Standard Library Function for files

23%

50%

16. Definition of stack and few examples

17. The operations of stack, Testing for exceptional cases 18. Representation of stacks in C 19.

Unit III 5.The stack

T2:Page #77-84,86-106 R1:page#150-1513-

162,163-173 Discussion of Infix, Postfix and Prefix expressions,

17% 64%

20. Recursion definition and the process of recursion 21. Recursion in ‘C’ and writing recursive programs,

Efficiency of Recursion 22. Iteration versus Recursion 23.

Unit IV 6.Recursion

T2:Page #117-125,127-134,142-146

R1:Page # 269-271,273,275-277,288,289

Properties of recursion.

7% 71%

24. Queues and its sequential representation 25.

7.Queues: T2:Page #174-175,177-

184,186-202,203-217,228-232,237-239 R2:Page # 127-138

Priority Queue, Array implementation of a priority 12% 80%

26. Linked list in C, 27. An example-Simulation using Linked list. 28. Linked List: implementation with and without header

nodes 29. Linked Implementation of Stack. 30. Linked Implementation of Queue 31. List operations like in searching and removing nodes

from List etc. 32. List in C: Array implementation of Lists. 33. Queues as list in C 34. Non integers and homogeneous list 35. Other List structure: Circular lists. 36. Other list structure: Doubly linked list 37.

Unit V & VI: 8 & 9.Lists T2:Page #186-202,203-217,228-231,237-239

R2:Page #152-159,161,188-200

Other examples.

17% 88%

38. Binary trees and its associated definitions 39. Binary search tree definition 40. Binary search tree definition and its implementation 41.

Unit VII & VIII 10 & 11.Trees

Other representation of trees such as using father field


etc.. 42. Tree traversal definitions (pre, in and post traversals) 43. Implementation of tree travels using recursion 44. Implementation of tree travels using recursion 45. Iterative in order tree traversal 46. Threaded binary tree definition and its implementation 47. Threaded binary tree definition and its implementation 48. Representation of trees and their application 49. Other examples. 50. Review. 51. Review. 52.

T2:Page #249-260,261-277,305,318

R1:Page #298-305,306-310

Review of question papers.

15%

100 %

Literature

Publication Info Book Type

Code Title & Author Edition Publisher Year

Text book

T1 Computer science A Structured Programming Approach Using C Behrouz A.Forouzan and Richard F. Gilberg

2nd THOMSON 2003

Text book

T2 Data structures using C & C++ by Yedidyah Langsam, Moshe J Augenstein & Aaron M Tanenbaum

2.1 Tata Mc-GrawHill

2002

Reference

R1 Data structure A Pseudo code approach with C 2nd Thomson 2005

Reference

R2 Data structures and Program Design using C by Robert L Kruse

2nd Eastern Economy

2001

Syllabus for test :

Test # Syllabus

T1 Class # 01 to 12

T2 Class # 13 to 25

T3 Class # 26 to 52

REVIEW OF STRUCTURES AND POINTERS, INTRODUCTION TO SPECIAL FEATURES OF C OBJECTIVE: • Learn : • Usage of structures, unions - a conventional tool for handling a group of logically related items. • Unions - sharing of memory. • Pointers - the real power of C.

1. What are structures? 2 2. Explain how the structures are useful by giving various examples. 4 3. Bring out the differences between structures and unions. 4 4. What is a pointer and why is it used? 4 5. With an example explain how bit fields can be defined in C. 4 6. What are enumerated data types? Explain with an example 4 7. List the various kinds of preprocessor statements. 4 8. What is the difference between macros and inline functions? 4 9. Explain the differences between malloc() and calloc() functions used for memory allocation 4 10. What is type casting? Give an example. 4 11. What are register variables? Where are they used? 4* 12. Why Macro is Need? Explain the conditional Macros with example. 5* 13. With the help of suitable example explain command line arguments 5* 14. Write a short note on Enumeration. 6* 15. Explain the storage classes. 6 16. What are macros? List few macros used in C. 6 17. What is union? How is it different from structure? With suitable example show how union is

declared and used in C? 6*


THE STACK OBJECTIVE:

• The most important concept in data structures. • To study the prominent role in the area programming is stack. • To expertise into a concrete and valuable tool in problem solving. 36 Define stack. Explain the implementation of various stack operations using structures. 4 37 Define stack. Explain the implementation of various stack operations using singly linked list. 4 38 Define stack. Explain the implementation of various stack operations using doubly linked list. 4 39 Explain how the stack is used in parameter passing. 4* 40 Write the prefix and postfix form of the following infix expressions

a) ((A + B) * C - (D-E)) $(F+G) b) (A+B)*(C+D-E)*F 4

41 Write a C function to convert a valid arithmetic infix expression into its equivalent postfix expression. Stack implementation is to be assumed

4*

43 Show the detailed concept of the stack to evaluate the following positive expression 632-5*+1^7+ *

4

44 Write short notes on dynamic stack representation. 5* 45 Show the detailed contents of the stack and trace of the algorithm to evaluate the given postfix

expression 123+*321-+* 5*

46 What is a stack? How it can be represented in "C" using arrays? 6* 47 What is a stack? Give examples to show the operations of stack. 6 48 Define Stack as a data structure and discuss its applications 6* 49 Obtain prefix and postfix expression

(A+B)*(C+D)$(A+B) A+B*C-D/E*H (A+B^C^D)*(E+F/D)

6*

50 What is stack? List the applications of stack. Write a ‘C’ function to insert an element on the top of stack.

6*

51 Implement the stack using arrays. 8 52 List the various ways of representing the arithmetic expressions by giving suitable examples 8 53 Show the detailed contents of the stack for given postfix expression to evaluate

6 2 3 + - 3 8 2 / + * 2 $ 3 + 10*

54.

List applications of stack. Using stack write an algorithm to determine if a given string is palindrome and print suitable message as output.

10*

55. Implement stack using static and dynamic memory allocation. Discuss the relative merits of these two implementations.

10*

18. What is a Macro definition? Write a C program to print the cube of a given number using a Macro definition.

6*

19. What do you understand by dynamic memory allocation? Explain any three functions that support dynamic allocation?

6*

20. What are bit wise operator? Give example for each operator 6 21. Write a program to copy contents of a file to another using command line arguments. 8 22. Write a program to merge the contents of a file to another using command line arguments. 8 23. What is the difference between macros and inline functions? 8 24. What are command line arguments? Write a C program to copy contents of a file to another file. 8* 25. What are the command line arguments? Write a C program to accept the file name and text

through command line arguments? Create a file with text and print the text on the screen 8*

26. Show the output of the following assuming a = 4, b = 3, c = 10 a) d = a & b b) d = a/b c) d = a^b d) d = ~c e) d = a >> 2 f) d = a << 2

9*

27. What are files? Create a file called sem.txt to store semester performances of all branches. Also display the semester and the branch, which has performed the best.

10

28. Create a file for storing employee database. To this file include operations to add new employees, delete. Employees and search for a particular employee.

10

29. Explain the various access modes used for files in C. 10 30. Write a C program to copy the contents of one file into another 10* 31. Explain the bit wise operators with examples used in C. 10* 32. What are Macros? Explain with an example. 10* 33. Explain call by value and call by reference. Give two examples. Define formal and actual

parameters. 10*

34. What are preprocessor directives? Explain any two operations that can be done using preprocessor directives.

10*

35. Create a structure pointed by a pointer variable and allocate memory using malloc() and calloc() separately. Execute the code and note your observations.

10


56. Write a program to check whether a given expression is a valid postfix expression or not. If valid evaluate a 33333333333. Given postfix expression otherwise display a suitable message.

10

57 Write a program to check whether a given expression is a valid prefix expression or not. If valid evaluate a given prefix expression otherwise display a suitable message.

10

58 Write an algorithm to convert a given infix expression into postfix expression. 10 59 Write an algorithm to convert a given infix expression into prefix expression. 10 60 Write an algorithm for converting infix expression to post-fix expression. Trace the algorithm

indicating content of stack for expression (a-b)/(c*d)+e. 10*

61 Show that , how stack operations takes place for the conversion of infix to postfix expression. (( A-(B+C)) *D) $(E+F)

10*

62 Convert the following infix expression into a postfix expression (((A/(B*C))+(D*E))-(A*C)) A$B*C-D+E/F/(G+H)

10*

63 Write an algorithm to implement a stack of size N using an array. The elements in the stack are to be integers. The operations to be supported are PUSH , POP and DISPLAY. Take into account the exceptions of Stack overflow and underflow.

10*

64 What is STACK? Explain operation performed on STACK. Discuss how the stack structure can be used for Tower of Hanoi problem.

12*

RECURSION OBJECTIVE:

• Recursion the most powerful and one of the best programming tools of data structures. • Advantages and disadvantages of the same. • Applications. 65 What is recursion? 2 66 What is a recursive definition? Indicate its properties? 4* 67 What is recursion? Give the properties of a recursive definition of an algorithm. What are its

advantages? 5*

68 What is a recursion? Compare the recursive programs with iterative programs. 6* 69 Write a note on Efficiency of Recursion. 6* 70 Write a "C" recursive program to solve the tower of Hanoi problem. Give the trace for 3 disks. 8* 71 What is recursion? Explain with an example 8* 72 Bring out the differences between recursion and iteration. 8 73 Write a program to find GCD of 2 nos. using iterative and recursive techniques 8 74 Write a program to find the following using recursion: i)

Factorial of a given number ii) Fibonacci series up to a given number

8

75 Write a program to solve the towers of Hanoi problem 8 76 Define recursion. Write a recursive program to find the GCD of two numbers. 8* 77 Write recursive c routines

i) For computing the binomial coefficient of k term of an n degree polynomial ii) That accepts a non negative decimal integer as a parameter and writes out Its binary representation.

8+8*

78 What is recursion? Discuss an example which can be represented both recursively and iteratively. 8* 79 Write recursive function for:

i) Fibonacci series for nth number ii) Printing number in reverse order

(6+6)*

80 Write a recursive C function to find the n Fibonacci number. Explain with an example 10* QUEUES AND LISTS OBJECTIVE: a. QUEUES:

• To make a considerable exhaustive study of yet another data structure QUEUE. • To study various forms of implementation techniques of the Queues and their different types. • To study the applications.

b. LISTS: • To study exhaustive about lists viz. singly linked list, doubly linked list, circular list, circular doubled linked

list, their implementation techniques and applications. QUEUES

81 Distinguish between Ordinary queues and Circular queues. 4* 82 What are the advantages and disadvantages of linked lists over arrays? 4* 83 Define Priority queues and explain. 4*


84 Write a routine to insert an element in a ordinary queue. 8* 85 Write a note on a Priority queues. 8* 86 Write a program to implement a linear queue using arrays. 8 87 Write a program to implement a circular queue using arrays. 8 88 Write a program to implement a double-ended queue using arrays. 8 89 A circular queue has a size of 5 and has 3 elements 10,40 and 20,where F=2 and R=4. After

inserting 50 and 60,what is value of F and r. Trying to insert 30 at this stage what will happen? Delete 2 elements from the queue and insert 100. Show the sequences of steps with necessary diagrams with the value of F and R.

8*

90 Write a C Program to perform the following operations on a queue Insert Delete Display

8*

91 Write a c function i) to insert an element at the rear end of a queue ii) to delete an element from the front end of the queue

10*

92 What is circular queue? Write ‘C’ program to implement circular queue using arrays with operations of INSERT (), DELETE () and DISPLAY ().

10*

LISTS 93 Understanding list operations like concatenation, searching for a node etc. 8 94 Understanding the array implementation of list 8 95 What is a SLL? Write a program to implement stack as a singly linked list. 8 96 Write a program to create an on ordered link list. 8 97 Write an algorithm to find whether a given list is ordered or not. 8 98 Write a recursive search routine to search for a node in a SLL. 8 99 Write a program to find for a particular node (either the position or info of the node can be given)

in a SLL. 8

100 Write an algorithm to concatenate two lists (assume both are existing) 8 101 What do you understand by a linked list? Write a C function SEARCH (F, X) that accepts a printer P

to a list of integers and an integer X, and returns a pointer to a node containing X, if it exists, and the NULL pointer otherwise.

8*

102 What is a single linked list? Explain with an example how a single linked list can be used for sorting a set of N numbers.

8*

103 What are different types of linked list? Write a C function to count number or elements present in single linked list.

10*

104 Write advantages of doubly linked list over singly linked list. Write C function that will insert a given integer value into an ordered doubly linked list.

10*

105 Write a C function to a. To count number of nodes using singly linked list b. To concatenate two singly linked list, and then to sort the resultant list c. To reverse direction of singly linked list(as shown below)

Start

Start

12*

106 Explain merging of two lists which have been represented as i) Array ii) Linked list

12*

107 Write a program to represent a polynomial of single variable using linked list and perform the following functions a. Evaluation of polynomial b. Display the polynomial

12*

DOUBLY LINKED LIST

108 Knowing the doubly linked list definition and its implementation 6 109 Write a program to find for a particular node (either the position or info of the node can be given)

in a DLL circular 6

110 What are the advantages and disadvantages of doubly linked list? Also give its applications. 6* 111 Write a C function to insert and delete a node from the front end in case of doubly linked list. 8* CIRCULAR LIST

112 Implement a circular SLL with the header node containing the total no of nodes in the list. The node itself Consists of student details like reg no, name, marks etc.

6

A B C D

D C B A


113 What are the advantages of circularly linked list over a linear list? Write a c routine that concatenates two circular lists.

6*

114 Write C functions to perform the following operations: a. Create a circular single linked list b. Display Circular single linked list

8*

TREES OBJECTIVE:

• To study exhaustively regarding a tree, types of trees and focus only on BST (Binary search tree). • To study the implementation of BST. • About applications.

115 What is binary tree? 2 116 What are the differences between strictly binary tree and complete binary tree 4 117 What are the two conditions under which a binary tree becomes an almost complete binary tree? 4 118 Discuss the applications of trees 4* 119 Explain with suitable example the following traversals of a tree

i) Preorder and ii) In order 4*

120 Give examples to show the father, son, and descendent and ascendant nodes of a binary tree. 6 121 Given the following traversals

In order: E I C F J B G D K H L A Preorder: A B C E I F J D G H K L Construct a Binary Tree

6*

122 What is a TREE? Define the following a. Ancestor b. Descendants of node with respect to the TREE

6*

123 Explain various type of tree traversal with simple example. 6* 124 Write C functions for following tree traversals

i) Inorder ii) Preorder iii) Post order 6*

125 What is binary search tree? Create a BST. 8 126 Explain the different methods of representation of binary trees in "C". 8* 127 Write recursive C routines to traverse a binary tree in different ways. Assume the dynamic node

representation of a binary tree 8*

128 Define the following a. Strict binary tree b. Almost complete binary tree c. Ordered tree d. Right in threaded binary tree

8*

129 Construct a binary tree for the expression A + ( B-C)*(E+F)/G and draw the diagram showing each step. 8* 130 Explain one-way and two-way threading of binary trees 8* 131 Implement the sequential representation of a binary search tree 10 132 Write an algorithm to traverse the tree using father field 10 133 List the various tree traversal techniques giving examples 10 134 Implement the recursive tree traversal of in, pre and post order traversals 10 135 Write an algorithm for the iterative tree traversal. 10 136 What is a threaded binary tree? 10 137 Implement the in order threaded binary tree. 10 138 Define the following terms with appropriate sketches

a) Tree b) Directed tree c) Ordered tree d) Binary tree e) Spanning tree 10

139 Explain the different methods of binary tree representation 10* 140 Write an output after traversing of a given tree by

i) in order ii) Preorder traversing methods

10*


141 Write an algorithms for deleting node in a binary search tree for all the three cases 12* 142 Write a "C" program to I) Create; and ii) traverse a binary tree in three orders. 12* 143 Write a C Function to create expression TREE using postfix expression, and discuss how a postfix

expression can be transformed to its equivalent prefix expression 12*

Marks No of Questions 2 3 4 25 5 5 6 26 8 41 9 1 10 35 12 7

Total 143


06CSE36 : UNIX & Shell Programming

Faculty : No of Hours:52

% of Portions covered Class

# Chapter Title /

Reference Literature Topic to be covered Reference

Chapter Cumulative

1 T1 : 1.2 Introduction to Unix Operating System 2.17 % 2.17 % 2 3

T1 : 2.1 to 2.12 Unix Architecture and Command usage

4.34 % 6.51 %

4 5 6

T1 : 4.1 to 4.13 File system : discuss some of the basic commands required to operate on files 6.52 % 13.03 %

7 8

T1 : 6.1 to 6.8 Basic file attributes

4.34 % 17.37 %

9 10

T1 : 5.1 to 5.18 Handling ordinary files : continuation with the basic commands

4.34 % 21.71 %

11 12 13

T1 : 3.1 to 3.14 General Purpose utilities : extension to the basic commands that is discussed 6.52 % 28.23 %

14 15 16

T1 : 7.1 to 7.10 VI editor : one of the editor available in Unix.

6.52 % 34.75 %

17 18 19

T1 : 12.1 to 12.11 Simple filters : introduce you to the way that you can construct powerful Unix command lines by combining Unix commands.

6.52 % 41.27 %

20 21 22

T1 : 13.1 to 13.12 Filters using regular expressions : discussion about set of characters that specify a pattern. 6.52 % 47.79 %

23 24

T1 : 11.1 to 11.8 More file attributes

4.34 % 52.13 %

25 26 27 28 29 30 31 32 33 34 35

T1 : 14.1 to 14.18

Shell Programming : Basics of shell programming Fundamental data types Types of parameters Decision control structures Loop control structures Debugging shell programs Sample Programs

23.91 % 76.04 %

36 37 38 39

T1 : 9.1 to 9.14

Process : The only active entities in a UNIX system are the processes. Will study basics, process creation, background process etc. 8.69 % 84.73 %

40 41 42 43

T1 : 18.1 to 18.16

Awk – advanced filter. One of the most powerful text manipulation utility.

8.69 % 93.42 %

44 45 46

T1 : 19.1 to 19.19

Perl – The master manipulator Perl is a programming language. Intended to be practical (easy to use, efficient, complete) rather than beautiful (tiny, elegant, minimal).

6.52 % 99.94 %

47 48 49 50

Revision and previous years question paper discussion

51 52

Guest lecture


Literature :

Publication Info Book Type Code Title & Author Edition Publisher Year

Text book T1 “ UNIX – Concepts and Applications “, Sumitabha Das 4th McGraw Hill 2006 Reference R1 “ Unix & Shell Programming “, Behrouz A Forouzan and

Richard F Gilberg - Thomson 2005

Reference R2 “ Unix & Shell Programming “, M G Venkateshmurthy - Pearson Education

2005

Syllabus for test :

Test # Syllabus

T1 Class # 01 to 16

T2 Class # 17 to 35

T3 Class # 36 to 46

QUESTION BANK

BACKGROUND AND SOME BASIC COMMANDS: OBJECTIVE: UNIX as the world knows it today is the happy outcome of the proverbial rags to riches story. Its Origin can be traced back to 1965, when a joint venture was undertaken by BELL telephone Laboratories, the GE company and MIT (USA). This chapter introduces the fundamental UNIX concepts, the major features of UNIX operating system & the Equipment. This chapter also deals with the difference with external and internal commands, the break up of a command into its arguments and options. This chapter introduces some of the general purpose utilities like cal, date etc.

1. Give the meaning of absolute and relative path names. 05*

2. Explain the architecture of the UNIX operating system. 05*

3. Discuss the salient features of UNIX system. 05*

4. Discuss the commands using which one can a) Know the users who are using the system at present b) Know the terminal setting and change them , if required c) Record a session

10*

5. With a neat diagram, explain the relationship between the kernel and the shell of UNIX 08*

6. How is the current directory indicated in the value of the PATH? 05

7. What is a pager? Name the two standard pagers used by man. 05

8. With block diagram explain Unix operating system organization and explain kernel-shell relationship?

10

9. What are salient features of Unix operating system? 10

10. Explain the multi-user capability of Unix? 10

11. What are the internal and the external commands in Unix? Explain three of them each, with examples?

10*

12. What is the difference between arguments and an option? Explain with example? 10

13. Explain the following? a) /bin b) /usr/bin c) tmp d) /etc

10

14. Explain the following? 10


a) cal b) date c) echo d) printf e) bc f) script

15. With examples, explain the date and lock commands. 04*

16. Write a note on the man command. 04*

THE FILE SYSTEM AND SOME FILE HANDLING: OBJECTIVE: The file system in UNIX is one of its simple and conceptually clean features. It lets users Access other files not belonging to them, and with out infringing on the security. This chapter deals with how to create directories, move around within the system, and list filenames in these directories. This chapter also deals with simple file handling commands that dos environment also offers except that the UNIX variety has more features

17. Write a note on the compression & decompression utilities available in UNIX. 8*

18. Explain the command using which two or more files can be concatenated. Hence or otherwise write a command line to concatenate two files fool and fooz with some text input from the terminal inserted between the contents of these two files. The output has to be stored on a file called fooz. Explain the command line written by you.

10*

19. Mention the different file comparing commands that you know. Explain the one that is used to print out the common entries on two sorted files.

6*

20. What is a file? 5

21. Explain the parent child relationship in unix file system. 8

22. Explain the following a) cd b) mkdir c) pwd d) rmdir

8

23. What are absolute path names? 8

24. What are relative path names? 8

25. Define the following file commands a) cat b) cp c) rm d) more

8

26. Explain the commands used in compressing and archiving files. 8

27. Define ordinary file, directory file, and device file. 10

28. Explain the following ls options a)output in multiple columns b) identifying directories and executables c) showing hidden files c) displaying the i node number

10

29. Define the following file commands a) lp b) wc c) od d) cmp e) comm f) diff

10

30. Mention the different categories of files that exist in UNIX. Discuss each one of them very briefly.

08*

31. What is the use of the following directories? Explain. i) /bin ii) /usr/bin iii) /mnt iv) /tmp v) /etc vi) /usr.

06*

FILE ATTRIBUTES: OBJECTIVE: The UNIX file system lets users access other files not belonging to them- without infringing on security. A file has a number of attributes that are changeable by well defined rules, this chapter deals with two basic file attributes – permissions and ownership. This chapter also deals with the seven fields of ls –l output.

32. Interpret the significance of the seven fields of the ls-l output. 8*

33. Write a command line using which one can assign all permissions to the owner of a file and assign only read permission to group and others.

4*

34. Define the following commands a) chown b)chgrp

5

35. What are relative permissions? 5

36. What are absolute permissions? 5

37. Define the different file permissions. 8

38. Define the command chmod. 8

39. How is chown different from chrgp when comes to renouncing ownerships. 10

40. Show the octal representation of these permissions a)rwxr-xrw b)rw-r----- c) –x-w-r--

10

41. Explain briefly the significance of the four fields of the ls -1 output. Who can change these 10


attributes? Is there any attribute can be changed only by the super user.

42. What is file permission? What are the different ways of setting file permission? Explain 06*

THE VI EDITOR: OBJECTIVE: The UNIX provides a versatile editor vi. The program is standard on all UNIX systems. This chapter discusses the features of vi editor.

43. Explain the three modes of the vi editor. 10 *

44. Clearly differentiate between hard links and soft links. 6*

45. Explain how one can customize his or her vi editing environment. 6*

46. What does the following command do when editing with vi:4, 8s / Unix/UNIX/ gc 5*

47. What is the significance of the n and N commands? 5

48. Name three ways exiting a vi session after saving your work. 8

49. Explain the commands used for entering and replacing test in input mode. 10

50. Explain the commands used in saving text and quitting in the ex mode. 10

51. Explain the functions of the command mode. 10

52. How will you replace has with have in the current line? 10

53. How will you insert a line a) above the current line b) below the current line? 10

54. Name the sequence of commands to execute to move to the line containing the string #include, deleting four lines there, and then replacing the deleted lines a the beginning of the file.

10

THE SHELL: OBJECTIVE: This chapter introduces shell. The shell is a unique and multifaceted program. It is a command interpreter and a programming language rolled into one. It is also a process that creates an environment for us to work on. This chapter focuses on the shell’s basic imperative activities.

55. Devise suitable wild card to match the following filenames

a) foo1 foo2 and foo5 b) quit.c, quit.o and quit.h c) tutorial ps and tutorial pdf d) all filenames beginning with dot and ending with .swp

10*

56. Explain the significance and usage of the following two special files: a)/dev/null b) /dev/tty

6*

57. Mention some of the wild cards that could be used with the shell and explain the special meanings associated with them in the shell environment. If required how can you despecilize the wild cards.

6*

58. Write a command line to execute a file called myscript on all week days, every half hour once between 9 and 17 hours.

5*

59. What is the significance of the command ls *.* 5

60. How do you find out the number of users logged in? 5

61. How do you remove only the hidden files of your directory? Does rm * remove theses files as well?

10

62. Match the filenames chapa, chapb, chapx, chapy and chapz with a wild card expression. 10

63. Name the three sources of standard input and output. 10

64. How do you save your entire home directory structure including the hidden files in a file? 10

65. The command, cat and bc, when used without arguments don’t seem to do anything. What does that indicate and how do you return shell prompt?

10

66. When the shell finds meta characters in the command line, what does it do? When the command is finally executed.

10

67. How do commands wc foo and wc < foo differ? Who opens the file in each case? 10

68. You have a file named * and a directory named My documents in the current directory. How will you remove them?

10

69. What is standard input and output? How do you achieve redirection using pipes and tees? Explain with an example.

06*


THE PROCESS: OBJECTIVE: A process is a UNIX abstraction that enables us to look files and programs in another way. A file is treated as a simple file when it lies in a dormant state on the disk. It can also be understood as a process when it is executed. UNIX being a multi tasking system, hundreds of processes run on a large system. Processes belong to the domain of the kernel which is responsible for their management. This chapter describes the kernels role in process management and the similarities between files and processes. This chapter also examines the process attributes and the inheritance mechanism at work and also examines process scheduling facilities offered by UNIX.

70. How is a process created? Mention briefly the role of fork and exec system calls in the process

creation. 8*

71. What is a process? Discuss the mechanism of a process creation in UNIX. 08*

72. Define job. How is job control done in UNIX? 6*

73. What is the significance of the PID and PPID? 5

74. Which processes do you think may have the maximum number of children? 5

75. How shell is created? 5

76. Explain the command kill. 5

77. Name some command that don’t require a separate process. 5

78. How will you kill the last background job without knowing its PID? 5

79. Explain the command ps along with its options. 10

80. What are system processes? 10

81. Explain the mechanism of process creation. 10

82. What are internal and external commands? 10

83. How do you run jobs in the background? 10

84. Explain the commands a) batch b) crontab c) time

10

COMMUNICATION IN UNIX: OBJECTIVE: In a multi-user system, it’s often necessary for one user to know what other is doing. Communication through the system seems quite natural and necessary, especially when users are located quite a distance apart. UNIX provides a few “real-times” communication tools and an impressive collection of email agents as offline communication tools. This chapter discusses two offline tools (finger and talk) and also email.

85. What is the default location of a user’s mail box on UNIX and LINUX systems? 5

86. Why is pine so useful on the internet? 5

87. Explain the significance of the terms mailbox and mbox. 5

88. What is a multipart mail message? 5

89. Explain the usage of the commands a)finger b) talk c)mesg

10

90. When do you use mailx with and without an argument? 10

91. Name two features of pine not found in mailx. 10

92. How will you call up pine so that it first shows the address book and not the main menu? 10

93. Explain wall, talk and mail commands as related to communication under UNIX OS. 06*

SIMPLE FILTERS AND GREP FAMILY OF COMMANDS: OBJECTIVE: This Chapter features simple filters of the system – commands which accept data from standard input, manipulate it and write the results to standard output. Filters are central tools of the UNIX tool kit, and each filter featured in this chapter performs a simple function. This chapter also discusses two more filters grep and sed.

94. Write a note on sort. 6*

95. How do you locate lines containing the following patterns using grep: a) sexena or saksena b) rajiv, rajeeb or rajeev c) SIGSTOP or SIGTSTP.

8*

96. Explain the grep command along with some of the options that would be used with it. 8*

97. Write a sample database file called mybase.lst that contains 4 records each having 4 fields with the 3rd field being the total masses field. With reference to this file with the names of the

8*


highest scores appearing first.

98. What is here document? Explain. 5*

99. What happens when you use head with multiple filenames. 5

100. Use head and tail to select lines 5 to 10 from q file. 5

101. What is the difference between a wild card and a regular expression? 5

102. Explain the following commands along with their options a) pr b) head c) tail d) cut.

10

103. Explain the following commands along with their optons a) paste b) sort c) uniq d) tr.

10

104. How will you use pr, sort and cut to read a file’s lines in reverse order? 10

105. Explain the grep command with options. 10

106. What do these commands do a) grep a b c b) grep <HTML> foo.

10

107. Explain the grep, egrep, fgrep with examples. 06*

108. Explain the following with examples: Pr, head, tail, cut, paste, sort.

06*

SHELL PROGRAMMING: OBJECTIVE: The activities of the shell are not restricted to command interpretation alone. The shell has a whole set of set of internal commands that can be strung together as a language- with its own variables, conditionals and loops. Shell programs are powerful because the external UNIX commands blend easily with the shell’s internal constructs. This chapter focuses on the Bourne shell- the lowest common denominator of all shells.

109. Develop a script logic that allows only Romeo and Henry to execute a program, and only from

the terminals tty05 and tty06. 10*

110. Display the processes in the system every 30 secs five times using a i) while loop ii) for loop. What is the unusual feature of the for loop?

6*

111. Explain the use of test and [ ] to evaluate expressions in shell. 8*

112. Explain the local and global variables in shell scripts. 6*

113. How do you input data to a shell script interactively? Discuss. 6*

114. Write a shell script that accepts any number of arguments and prints them in the reverse order. For example if the input arguments are x y z then the output produced should be z y x.

8*

115. Explain the expression command. 6*

116. Compare shell scripts and system calls. 5

117. Write a shell script to search a given pattern in a file? 5

118. Write a short note on Bourne shell? 5

119. What is exit status of a command? What is its normal value and where is the value stored? 5

120. What is a here document? Explain with an example. Also mention its use. 06*

121. What is for loop in a shell script? Write a script to display the processes in a system every 30 sec.

6

122. What is a shell program? What are different ways of executing shell program? Explain. 8

123. Write a shell script to create a menu which displays the list of files, current data, process status and current users of the system.

8

124. How will you list various file attributes while writing shell scripts? 8

125. Demonstrate the use of a) if statement b)while loop in developing the shell’s scripts ? give suitable examples

10

126. What do you mean by exporting shell variables? explain with examples. 10

127. What do you mean by command line argument in shell scripts? How are these arguments handled?

10

128. Write a shell script to accept a string from the terminal and echo a suitable message if it doesn’t have at least 10 characters using a) case b) expr

10

129. Write a script that accepts a filename name as a argument and displays the last modification time if the file exists and a suitable message if it doesn’t.

10

130. Write a script that accepts one or more filenames as arguments and converts them all to uppercase provided they exist in the current directory.

10

131. Devise a script that takes a filename as argument and locates from your home directory tree all pathnames of its links. The list should be mailed to self.

10


132. Devise a script that allows a user to view, add, delete or modify a setting in a configuration file that contains these settings in the form variable = value.

10

133. Devise a script that creates a lock file which prevents more than one user from running it. The lock file must be removed before script termination or if the user presses the interrupt key.

10

134. What is here document? Explain with an example. Also mention its use. 06* AWK: OBJECTIVE: The awk command made a late entry into the UNIX system in 1977 to augment the tool kit with suitable report formatting capabilities. Awk until the advent of perl was the most powerful utility for text manipulation. Unlike filters awk operates on the field level and can access and can easily access, transform and format individual fields in a line. This chapter discusses important features of awk in detail. This helps in understanding perl, which uses

most of tea wk constructs.

135. Use awk to locate lines longer than 100 and smaller than 150 characters. 10

136. Use a for loop to center the to center the output of the command echo “document list” where page width is 55 characters.

10

137. Use a script to kill a process by specifying its name rather than the PID. 10

138. Write an awk sequence in a shell script which accepts input from the standard input. The program should print the total of any column specified as a script argument. For instance, prog1 | awk_prog 3 should print the total of the third column in the output of prog1.

10

139. Find out the next available UID in etc/passwd after ignoring all system users placed at the beginning and up to the occurrence of the user nobody.

10

140. Find out recursively the files in your home directory that have been last modified on January 6 of the current year at the 11ty hour.

10

141. The tar command on one system can’t accept absolute path names longer than 100 characters. How can you use find and awk to generate a list of such files?

10

142. Write an awk sequence to find HRA DA and the net pay of an employee where DA is 30 % of basic, HRA is 10 % of basic and net pay is the sum of HRA, DA and the basic pay with suitable headings.

10*

143. What is the difference between print and print $0? 5

144. Explain the awk function that is used to determine the length of a record on a file , say, marks .pu assume that the record number is 15.

5*

145. State any 6 built-in variables in awk and explain each with an example. 6*

146. Discuss the operational mechanism of awk. 6*

PERL: OBJECTIVE: Perl is the UNIX’s latest major acquisition and one of its finest. perl combines the power of some of the most powerful unix tools – the shell, grep, tr, sed and awk. It has all control structures that you could possibly have seen anywhere. It has a host of other features related to handling of files, directories processes and so on. This chapter discusses features of perl.

147. Explain how perl handles list? 10

148. Using command line arguments write a perl program to find whether a given year is a leap year. 10

149. How arrays are handled in perl? Explain. 10

150. Explain the variables and operators used in perl. 10

151. Explain with examples the handling of subroutines in perl. 10

152. Explain the string handling functions in perl. 10

153. Print the string UNIX 20 times without using a loop. 10

154. How will you print only the first occurrence of a string in a file? 10

155. How will you use find and perl to delete all files modified more than a year back? What is the advantage of using this method compared to using find with –exec rm?

10

156. How will you use perl script to convert a binary number (supplied as an argument) to a decimal. 10*

157. Write a program that prompts a user to input a string and a number and prints the string that many times with each string on a separate line.

10*

158. Explain the chop () and chomp () functions in perl. 5*

159. With the aid of a simple example explain the split function as available in perl. 5*

160. Explain file handling in perl. 6*


06CSEL37 : DATA STRUCUTRES LAB

Class no Programs to be covered 1 Program no 1 2 Program no 2, 3 3 Program no 4,5 4 Program no 6 5 Program no 7, 8 6 Program no 9 7 Program no 10, 11 8 Program no 12 9 Program no 13 10 Program no 14 a, 14 b

LIST OF PROGRAMS

1 Write a program to create a sequential file with at least five records, each record having the structure shown below :

2 Write and demonstrate the following functions: a.newStrCpy that does the same job as strcpy. b.newStrCat that does the same job as strcat. Without using any library function.

3 Write a C Program which accepts the Internet Protocol(IP) Address in decimal dot format.(ex.153.18.8.105) and converts it into 32 bit long integer(ex.2568095849) using strtok library function and unions.

4 Write a C program to construct a stack of integers and to perform the following operations on it. a) Push b) pop c)display

The program should print appropriate messages for stack overflow, stack underflow and stack empty. 5 Write a C program to convert and print a given valid parenthesized infix arithmetic expression to

postfix expression. The expression consists of single character operands and the binary operators + (plus), - (minus), * (multiply) and / (divide)

6 Write a C program to evaluate a valid suffix / postfix expression using stack. Assume that the suffix / postfix expression is read as a single line consisting of non negative single digit operands and binary arithmetic operators. The arithmetic operators are + (ADD), - (SUBTRACT), * ( MULTIPLY) and / (DIVIDE)

7 Write a C program to simulate the working of a queue of integers using an array. Provide the following operations :

a) Insert b) delete c) display 8 Write a C program to simulate the working of a circular queue of integers using an array. Provide the

following operations : a) Insert b) delete c) display

9 Write a program using dynamic variables and pointers, to construct a singly linked list consisting of the following information in each node : student id ( integer ), student name ( character string ) and semester ( integer ). The operations to be supported are :

a) The insertion operations. b) The Deletion operations. b) c) Searching Operation. d) Displaying all the nodes in the list.

10 Write a program using dynamic variables and pointers, to construct a singly linked list to perform the operations of a stack of integers :

a) Push b) pop c) display 11 Write a program using dynamic variables and pointers to construct a queue of integers using singly

linked list and to perform the following operations : a) Insert b) delete c) display

12 Write a program to support the following operations on a doubly linked list where each node consists of integers. a) Create a doubly linked list. b) Delete the node of a given data. c) Display the content of the list.

13 Write a program to : a) To construct a binary search tree of integers. b) Top traverse the tree using all the methods i.e inorder, preorder and postorder to display the

elements in the tree 14 a Write a program to search for an element using binary search. 14 b Write a recursive C program for solving Tower of Hanoi problem.


06CSEL38 : Electronic Circuits & Logic Design Laboratory

Part A : Expt

# Program

a. To study the working of positive clipper, double –ended clipper and positive clamper using diodes.

1.

b. To build and simulate the above circuits using a simulation package a. To determine the frequency response, input impedance, output impedance, and bandwidth of a CE amplifier.

2.

b. To build the CE amplifier circuit using a simulation package and determine the voltage gain for two different values of supply voltage and for two different values of emitter resistance. a. To determine the drain characteristics and transconductance characteristics of an enhancement-mode MOSFET

3.

b. To implement a CMOS inverter using a simulation package and verify its truth table a. To design and implement a Schmitt trigger using Op-Amp for given UTP and LTP values. 4. b. To implement a Schmitt trigger using Op-Amp using a simulation package for two sets of UTP and LTP values. a. To design and implement a rectangular waveform generator (Op-Amp relaxation oscillator) for given frequency.

5.

b. To implement a rectangular waveform generator (Op-Amp relaxation oscillator) using a simulation package and observe the change in frequency when all resistor values are doubled.

6. To design and implement an astable multivibrator circuit using 555 timer for a given frequency and duty cycle.

7. To implement a +5V regulated power supply using full-wave rectifier and 7805 IC regulator in simulation package. Find the output ripple for different values of load current.

Part B : Expt

# Program

a. Given any 4-variable logic expression, simplify using Entered Variable Map and realize the simplified logic expression using 8:1 multiplexer IC.

1.

b. Write the Verilog /VHDL code for an 8:1 multiplexer. Simulate and verify its working. a. Realize a full adder using 3-to-8 decoder IC and 4 input NAND gates. 2. b. Write the Verilog/VHDL code for a full adder. Simulate and verify its working. a. Realize a J-K Master/Slave Flip-Flop using NAND gates and verify its truth table. 3. b. Write the Verilog/VHDL code for D Flip-Flop with positive-edge triggering. Simulate and verify its working. a. Design and implement a mod-n (n<8) synchronous up counter using J-K Flip-Flop ICs. 4. b. Write the Verilog/VHDL code for mod-8 up counter. Simulate and verify its working. a. Design and implement a ring counter using 4-bit shift register. 5. b. Write the Verilog/VHDL code for switched tail counter. Simulate and verify its working.

6. Design and implement an asynchronous counter using decade counter IC to count up from 0 to n (n<=9).

7. Design a 4-bit R-2R ladder D/A converter using Op-Amp. Determine its accuracy and resolution.

Note 1. Any simulation package like MultiSim / Pspice etc. may be used. 2. In the practical examination all students in batch will pick up one question from the diminishing lot that initially contained all the 14 questions.

All Sub Ques

Documents

3rd semester

heat equations

cosine transforms

range sine

homogeneous

fourier series

fourier series

hasse diagram