Digital Principles UNIT 1 Final

UNIT 1

2 MARKS QUESTIONS AND ANSWERS

1.Define the term digital.

The term digital refers to any process that is accomplished using discrete

units

2.What is meant by bit?

A binary digit is called bit

3.What is the best example of digital system?

Digital computer is the best example of a digital system.

4.Define byte?

A group of 8 bits.

5.List the number systems?

i) Decimal Number system

ii) Binary Number system

iii) Octal Number system

iv) Hexadecimal Number system

6.State the sequence of operator precedence in Boolean expression?

i) Parenthesis

ii) AND

iii) OR

7.What is the abbreviation of ASCII and EBCDIC code?

ASCII-American Standard Code for Information Interchange.

EBCDIC-Extended Binary Coded Decimal Information Code.

8.What are the universal gates?

NAND and NOR

9.What are the different types of number complements?

i) r’s Complement

ii) (r-1)’s Complement.

10.Why complementing a number representation is needed?

Complementing a number becomes as in digital computer for simplifying the

1

subtraction operation and for logical manipulation complements are used.

11.How to represent a positive and negative sign in computers?

Positive (+) sign by 0

Negative (-) sign by 1.

12.What is meant by Map method?

The map method provides a simple straightforward procedure for

minimizing Boolean function.

13.What is meant by two variable map?

Two variable map have four minterms for two variables, hence the map

consists of four squares, one for each minterm

14.What is meant by three variable map?

Three variable map have 8 minterms for three variables, hence the map

consists of 8 squares, one for each minterm

15.Which gate is equal to AND-inverter Gate?

NAND gate.

16.Which gate is equal to OR-inverter Gate?

NOR gate.

17.Bubbled OR gate is equal to--------------

NAND gate

18. Bubbled AND gate is equal to--------------

NOR gate

19.What is the use of Don’t care conditions?

Any digital circuit using this code operates under the assumption that these

unused combinations will never occur as long as the system

20.Express the function f(x, y, z)=1 in the sum of minterms and a product of

maxterms?

Minterms=_(0,1,2,3,4,5,6,7)

Maxterms=Nomaxterms.

21.What is the algebraic function of Exclusive-OR gate and Exclusive-NOR gate?

F=xy’ + x’y

F=xy +x’y’

2

22.What are the methods adopted to reduce Boolean function?

i) Karnaugh map

ii) Tabular method or Quine mccluskey method

iii) Variable entered map technique.

23.Why we go in for tabulation method?

This method can be applied to problems with many variables and has the

advantage of being suitable for machine computation.

24.State the limitations of karnaugh map.

i) Generally it is limited to six variable map (i.e.) more then six variable

involving expressions are not reduced.

ii) The map method is restricted in its capability since they are useful for

simplifying only Boolean expression represented in standard form.

25.What is tabulation method?

A method involving an exhaustive tabular search method for the minimum

expression to solve a Boolean equation is called as a tabulation method.

26.What are prime-implicants?

The terms remained unchecked are called prime-implecants. They cannot be

reduced further.

27.Explain or list out the advantages and disadvantages of K-map method?

The advantages of the K-map method are

i. It is a fast method for simplifying expression up to four

variables.

ii. It gives a visual method of logic simplification.

iii. Prime implicants and essential prime implicants are identified

fast.

iv. Suitable for both SOP and POS forms of reduction.

v. It is more suitable for class room teachings on logic

simplification.

The disadvantages of the K-map method are

i. It is not suitable for computer reduction.

ii. K-maps are not suitable when the number of variables

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involved exceed four.

iii. Care must be taken to fill in every cell with the relevant entry,

such as a 0, 1 (or) don’t care terms.

28.List out the advantages and disadvantages of Quine-Mc Cluskey method?

The advantages are,

a. This is suitable when the number of variables exceed four.

b. Digital computers can be used to obtain the solution fast.

c. Essential prime implicants, which are not evident in K-map, can be

clearly seen in the final results.

The disadvantages are,

a. Lengthy procedure than K-map.

b. Requires several grouping and steps as compared to K-map.

c. It is much slower.

d. No visual identification of reduction process.

e. The Quine Mc Cluskey method is essentially a computer reduction

method.

29.Define Positive Logic.

When high voltage or more positive voltage level is associated with binary ‘1’

and while the low or less positive level is associated with binary ‘0’ then the system

adhering to this is called positive logic.

30.Define Negative Logic.

When high voltage level is associated with binary ‘0’ and while the low level

is associated with binary ‘1’ then the system adhering to this is called negative logic

31.Why parity checker is needed?

Parity checker is required at the receiver side to check whether the expected

parity is equal to the calculated parity or not. If they are not equal then it is found

that the received data has error.

32.What is meant by parity bit?

Parity bit is an extra bit included with a binary message to make the number

of 1’s either odd or even. The message, including the parity bit is transmitted and

then checked at the receiving and for errors.

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33.Why parity generator necessary?

Parity generator is essential to generate parity bit in the transmitter.

34.What is IC?

An integrated circuit is a small silicon semiconductor crystal called a chip

containing electrical components such as transistors, diodes, resistors and

capacitors. The various components are interconnected inside the chip to form an

electronic circuit.

35.What are the needs for binary codes?

a. Code is used to represent letters, numbers and punctuation marks.

b. Coding is required for maximum efficiency in single transmission.

c. Binary codes are the major components in the synthesis (artificial

generation) of speech and video signals.

d. By using error detecting codes, errors generated in signal transmission

can be detected.

e. Codes are used for data compression by which large amounts of data are

transmitted in very short duration of time.

36.Mention the different type of binary codes?

The various types of binary codes are,

f. BCD code (Binary Coded decimal).

g. Self-complementing code.

h. The excess-3 (X’s-3) code.

i. Gray code.

j. Binary weighted code.

k. Alphanumeric code.

l. The ASCII code.

m. Extended binary-coded decimal interchange code (EBCDIC).

n. Error-detecting and error-correcting code.

o. Hamming code.

37.List the advantages and disadvantages of BCD code?

The advantages of BCD code are

a. Any large decimal number can be easily converted into corresponding

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binary number

b. A person needs to remember only the binary equivalents of decimal

number from 0 to 9.

c. Conversion from BCD into decimal is also very easy.

The disadvantages of BCD code are

a. The code is least efficient. It requires several symbols to represent

even small numbers.

b. Binary addition and subtraction can lead to wrong answer.

c. Special codes are required for arithmetic operations.

d. This is not a self-complementing code.

e. Conversion into other coding schemes requires special methods.

38.What is meant by self-complementing code?

A self-complementing code is the one in which the members of the number

system complement on themselves. This requires the following two conditions to be

satisfied.

a. The complement of the number should be obtained from that number

by replacing 1s with 0s and 0s with 1s.

b. The sum of the number and its complement should be equal to

decimal 9. Example of a self-complementing code is

i. 2-4-2-1 code.

ii. Excess-3 code.

39.Mention the advantages of ASCII code?

The following are the advantages of ASCII code

a. There are 27 =128 possible combinations. Hence, a large number of

symbols,alphabets etc.., can be easily represented.

b. There is a definite order in which the alphabets, etc.., are assigned to each

code word.

c. The parity bits can be added for error-detection and correction.

40.What are the disadvantages of ASCII code?

The disadvantages of ASCII code are

a. The length of the code is larger and hence more bandwidth is required

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for transmission.

b. With more characters and symbols to represent, this is not completely

sufficient.

41.What is the truth table?

A truth table lists all possible combinations of inputs and the

corresponding outputs.

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UNIT 1

16 MARKS QUESTIONS AND ANSWERS

1. Explain about the decimal number system.

Solution:

8

2. Explain about nine’s and ten’s compliment.

Solution:

3. Find the 9’s complioment of the following numbers.

(a) 3465 (b)782.54 (c)4526.075

Solution:

4. Find the 10’s compliment of the following numbers.

(a) 4069 (b) 1056.074

9

Solution:

5. Subtract the following numbers using 9’s compliment method.

(a) 745.81 - 436.62 (b) 436.62 – 745.81

Solution:

6. Subtract the following numbers using 10’s compliment method.

(a) 2928.54 – 416.73 (b) 416.73 – 2928.54

10

Solution:

7. Explain about binary number system.

Solution:

11

8. Convert the following binary numbers to decimal numbers.

(a) 101012 (b) 11011.1012

Solution:

(a)

12

(b)

9. Convert the following decimal numbers to binary numbers.

(a) 52 (b) 0.75 (c) 105.15

Solution:

(a)

(b)

13

(c)

10. Add the binary numbers 1101.101 and 111011.

Solution:

14

11. Subtract 111.1112 from 1010.012.

Solution:

12. Multiply 1011.1012 by 101.012

Solution:

15

13. Divide 110101.112 by 1012.

Solution:

14. Representation of signed numbers using the 2’s (or 1’s) compliment method.

Solution:

16

2’s compliment numbers have the following properties

Methods of obtaining the 2’s complement of a number

Express -45 in 8-bit 2’s compliment form.

17

Solution:

Express -73.75 in 12-bit 2’s compliment form.

Solution:

15. Add the following using 12-bit 2’s compliment arithmetic.

Solution:

(a) Add – 75 to + 26.

(b) Add – 45.75 to + 87.5.

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(c) Add 27.125 to – 79.625.

(d) Add – 31.5 to – 93.125.

(e) Subtract 14 from 46.

16. Add the following using 8-bit 1’s compliment arithmetic.

19

Solution:

(a) Add – 25 to – 14.

(b) Add + 25 and + 14.

17. Subtract 27.50 from 68.75 using the 12 bit 1’s compliment form

Solution:

18. Add – 89.75 to + 43.25 using the 12-bit 1’s compliment form.

Solution:

20

19. Convert 367.528 to binary.

Solution:

20. Convert 110101.1010102 and 10101111001.01112 to octal

Solution;

21. Convert 4057.068 to decimal.

Solution:

21

22. Convert 378.9310 to octal

Solution:

23. Add 327.548 to 665.378 and Subtract 16.478 to 20.148.

Solution:

22

24. Subtract 236.438 from 5427.658 using the 7’s compliment arithmetic and Subtract 5427.658 from 236.438 using the 8’s compliment method.

Solution:

23

25. Explain about hexadecimal number system.

Solution:

26. Convert 01011111011.0111112 to hexadecimal.

Solution:

24

\27. Convert 3A9E.B0D16 to binary.

Solution:

28. Convert A0F9.0EB16 to decimal.

Solution:

29. Convert 2598.67510 to hex.

Solution:

25

30. Convert 756.6038 to hex.

Solution:

26

31. Convert B9F.AE16 to octal.

Solution:

32. Add 2A7C.30D16 and 8D9.E8B16.

Solution:

33. Find the 15’s and 16’s compliment of the following hexadecimal numbers.

Solution:

27

34. Subtract 4AB.6B16 from 5074.5616 using the 15’s compliment method.

Solution:

35. Subtract 507D.5616 from 4AB.6816 using the 16’s compliment method.

Solution:

28

36. Subtract the following hexadecimal numbers using the 1’s compliment arithmetic.

Solution:

37. Subtract the following hexadecimal numbers using the 2’s compliment arithmetic.

Solution:

29

38. Explain about weighted and non weighted codes Solution:

30

39. Explain sequential codes, self complementing codes and cyclic codes.

Solution:

Sequential codes:

Self complementing codes:

Cyclic codes:

31

40. Explain about 8421 BCD code.

Solution:

BCD Arithmetic

41. Perform the following decimal additions in 8421 BCD code.

Solution:

32

42. Perform the following decimal subtractions in 8421 BCD code.

Solution:

43. Perform the following decimal subtractions in BCD by the 9’s compliment method.

Solution:

33

44. Perform the following decimal subtractions in BCD by the 10’s compliment method.

34

Solution:

45. Explain about EXCESS THREE (XS - 3) code.

Solution:

XS-3 Arithmetic

35

46. Perform the following addition in XS- 3 code.

Solution:

36

47. Perform the following subtraction in XS- 3 code.

Solution:

48. Explain about gray code.

Solution:

Binary to gray conversion

37

Gray to binary conversion

38

49. Convert the binary 1001 to gray code.

Solution:

50. Convert the gray code 1101 to binary.

Solution:

39

51. Explain about error detecting codes.

Solution:

Parity

40

52. Explain about different logic gates.

Solution:

a) The AND Gate:

41

b) The OR Gate:

c) The NOT Gate:

42

The Universal Gates:

d) The NAND Gate:

43

e) The NOR Gate:

44

f) The Exclusive – OR (X -OR) Gate:

g) The Exclusive – NOR (X - NOR) Gate:

45

53. Explain different Laws of Boolean Algebra.

Solution:

Commutative Laws:

46

Associative Laws:

47

Distributive Laws:

48

54. Explain about different rules in Boolean Algebra.

Solution:

49

55. Explain Duality Theorem And DeMorgan’s Theorem.

Solution: Duality Theorem:

DeMorgan’s Theorem:

50

56. State and prove Consensus Theorem:

Solution:

51

57. Reducing the Following Boolean Expressions:

52

53

58. Proove the Universality Property of NAND and NOR gates.

Solution:

NAND Gate:

NOT Function

54

AND Function

OR Function

55

NOR Function

56

NOR Gate:

NOT Function

OR Gate

57

AND Function

58

59. Simplify the following using DeMorgan’s theorems.

Solution:

59

60. Explain Sum Of Product and Product Of Sum forms.

Solution:

SUM OF PRODUCT FORM

PRODUCT OF SUM FORM

60

61. Explain about standard Canonical Form (Standard SOP and POS forms)

Solution:

Standard SOP Form or Minterm Canonical Form

61

Standard POS Form or Maxterm Canonical Form

Conversion of SOP to Standard SOP form

Conversion of POS to Standard POS form

62

62. Convert the given expression in standard SOP form.

Solution:

63

63. Convert the given expression in standard SOP form.

Solution:

64. Convert the given expression in standard POS form.

Solution:

64

65. Convert the given expression in standard POS form.

Solution:

65

66. M-Notations: Minterms and Maxterms.

Solution:

66

67

Truth Table 2

Compliments of canonical forms

68

67. Explain Karnaugh Map Minimization

Solution:

One-Variable, Two-Variable, Three-Variable and Four Variable Maps.

69

70

Representation of Truth Table on K-maps

71

72

73

68. Grouping Cells for Simplification.

Solution:

Grouping Two Adjacent Ones (Pair)

74

Grouping four Adjacent Ones (Quad)

75

Y=A Y=CD

Y=BD Y=AD’

76

69. Procedure to simplify Boolean expressions

Solution:

70. Minimize the expression

77



78


74. Reduce the following function using K-map.

79

75. Reduce the following function using K-map.

fig a.

Essential Prime Implicants:

Limitations of K-map

80

Quine-McCluskey, or tabular method

Algorithm for generatingPrime implicants

81

76. Simplify the following Boolean function using Quine-McCluskey, or tabular method

Solution:

82

table 2.4

77. Simplify the following Boolean function using Quine-McCluskey, or tabular method

83

Solution:

84

85

86