Lecture 1: Computer architecture

Technische Universität München

Section 1: Programming on a Section 1: Programming on a Section 1: Programming on a Section 1: Programming on a ComputerComputerComputerComputer

- What is a computer- What is required for calculation- A suitable representation of numbers- A rule set for the operations

(Boolean Algebra)- A (mechanical/electrical/)electronically

implementation

Section1-Page1

implementation- John-von-Neumann architecture


What is a computer

What does WIKIPEDIA say?“A computer is a general purpose device that “A computer is a general purpose device that can be programmed to carry out a set of arithmetic or logical operations.”http://en.wikipedia.org/wiki/Computer, 2013-10-20

Or the lexicon ITWissen (= “IT Knowledge”)?“Computer are [programmable] calculation machines to process calculation operations on the basis of a mechanical, an electrical or an

Section1-Page2

the basis of a mechanical, an electrical or an electronically unit. The DIN [German Industry Norm] defines a computer as an unit to process data to perform mathematical, converting, transferring or saving operations.”http://www.itwissen.info/definition/lexikon/Computer-computer.html, 2013-10-20



- What is a computer- What is required for that calculation- A suitable representation of numbers- A rule set for the operations


implementation

Section1-Page3



What is required for that calculation

1. Step: a suitable representation of numbers1. Step: a suitable representation of numbers

2. Step: a rule set for operations

3. Step: a mechanical/electrical/electronically implementation

Section1-Page4





implementation

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A suitable representation of numbers

e.g. the decimal system (with the base 10)

a) Positional numeral system, which represents each digit with one symbol digit with one symbol

b) Each digit represents one dedicated value in the represented number on the basis b , e.g. bp (p = 0,1,2,…)

0, 1, 2, 3, 4, 5, 6, 7, 8, 90, 1, 2, 3, 4, 5, 6, 7, 8, 90, 1, 2, 3, 4, 5, 6, 7, 8, 90, 1, 2, 3, 4, 5, 6, 7, 8, 9

Number: 2 3 0 4 5 Number: 2 3 0 4 5 Number: 2 3 0 4 5 Number: 2 3 0 4 5 ( = representation)( = representation)( = representation)( = representation)

100101102103104

Section1-Page6Rembold, Ulrich et. al.: Einführung in die Informatik für Naturwissenschaftler und Ingenieure. Hanser München Wien 1991

c) Each number representation is unique, including

the zero (= 0)

1010101010

5 * 100 = 5 * 1 = 54 * 101 = 4 * 10 = 40

0 * 102 = 0 * 100 = 03 * 103 = 3 * 1000 = 3000

2 * 104 = 2 * 10000 = 20000

= value= value= value= value


d) The representation supports mathematical (+, -,



d) The representation supports mathematical (+, -,

*, /, …) and logical (equal, <, >, …) operations

2 3 0 4 52 3 0 4 52 3 0 4 52 3 0 4 5+ 3 9 9+ 3 9 9+ 3 9 9+ 3 9 9

= 2 3 4 4 4= 2 3 4 4 4= 2 3 4 4 4= 2 3 4 4 411 Carry over

2 3 0 4 5 3 9 92 3 0 4 5 3 9 92 3 0 4 5 3 9 92 3 0 4 5 3 9 9>>>>


2 3 0 4 5 3 9 92 3 0 4 5 3 9 92 3 0 4 5 3 9 92 3 0 4 5 3 9 9Value of the number Value of the number>>>>


e) Fractional parts of a number can be represented,

e.g. using a point notation




f) Positive and negative numbers can be represented

Number: 1 . 2 4 3 Number: 1 . 2 4 3 Number: 1 . 2 4 3 Number: 1 . 2 4 3 ( = representation)( = representation)( = representation)( = representation)

10-310-210-1100

3 * 10-3 = 5 * 0.001 = 0.0034 * 10-2 = 4 * 0.01 = 0.04 2 * 10-1 = 0 * 0.1 = 0.2

1 * 101 = 1 * 1 = 1



f) Positive and negative numbers can be represented

---- 2 3 0 4 5 2 3 0 4 5 2 3 0 4 5 2 3 0 4 5 ---- 3 9 93 9 93 9 93 9 9+ 5 0 0 1+ 5 0 0 1+ 5 0 0 1+ 5 0 0 1

= sign= sign= sign= sign


BUT:BUT:BUT:BUT: difficult to be represented in a mechanical unit,difficult to be represented in a mechanical unit,difficult to be represented in a mechanical unit,difficult to be represented in a mechanical unit,e.g. with states on a mechanical boarde.g. with states on a mechanical boarde.g. with states on a mechanical boarde.g. with states on a mechanical board



e.g. with states on a mechanical boarde.g. with states on a mechanical boarde.g. with states on a mechanical boarde.g. with states on a mechanical board

0, 1, 2, 3, 4, 5, 6, 7, 8, 90, 1, 2, 3, 4, 5, 6, 7, 8, 90, 1, 2, 3, 4, 5, 6, 7, 8, 90, 1, 2, 3, 4, 5, 6, 7, 8, 9

EASIER: EASIER: EASIER: EASIER: a representation with only two states (digits)a representation with only two states (digits)a representation with only two states (digits)a representation with only two states (digits)

Section1-Page9Rembold, Ulrich et. al.: Einführung in die Informatik für Naturwissenschaftler und Ingenieure. Hanser München Wien 1991http://en.wikipedia.org/wiki/File:Jacquard.loom.cards.jpg, 2013-10-20

EASIER: EASIER: EASIER: EASIER: a representation with only two states (digits)a representation with only two states (digits)a representation with only two states (digits)a representation with only two states (digits)

0, 10, 10, 10, 1

Punch card Electric circuit


tttthe binary (digital) system (with the base 2)he binary (digital) system (with the base 2)he binary (digital) system (with the base 2)he binary (digital) system (with the base 2)

a) Positional numeral system, which represents each digit with one symbol


digit with one symbol


0, 10, 10, 10, 1

Number: 1 1 0 1 0 0 1 1 Number: 1 1 0 1 0 0 1 1 Number: 1 1 0 1 0 0 1 1 Number: 1 1 0 1 0 0 1 1 ( = representation)( = representation)( = representation)( = representation)

2021222324252627


1 * 20 = 1 * 1 = 11 * 21 = 1 * 2 = 20 * 22 = 0 * 4 = 00 * 23 = 0 * 8 = 0

1 * 24 = 1 * 16 = 160 * 25 = 0 * 32 = 01 * 26 = 1 * 64 = 64

1 * 27 = 1 * 128 = 128


ΣΣΣΣ 211211211211decdecdecdec


a) Positional numeral system, which represents each digit with one symbol



digit with one symbol


0, 10, 10, 10, 1


2021222324252627

ByteByteByteByte

BitBitBitBit


1 * 20 = 1 * 1 = 11 * 21 = 1 * 2 = 20 * 22 = 0 * 4 = 00 * 23 = 0 * 8 = 0

1 * 24 = 1 * 16 = 160 * 25 = 0 * 32 = 01 * 26 = 1 * 64 = 64

1 * 27 = 1 * 128 = 128



ByteByteByteByte


b) cont.



b) cont.Maximum number, represented with one byte:


2021222324

1 * 20 = 1 * 1 = 11 * 21 = 1 * 2 = 21 * 22 = 1 * 4 = 41 * 23 = 1 * 8 = 8

1 * 24 = 1 * 16 = 161 * 25 = 1 * 32 = 32


252627

ByteByteByteByte

BitBitBitBit


1 * 25 = 1 * 32 = 321 * 26 = 1 * 64 = 64

1 * 27 = 1 * 128 = 128


�� 0000decdecdecdec –––– 255255255255decdecdecdec

((((withoutwithoutwithoutwithout a a a a signsignsignsign))))


b) cont.



b) cont.

Used representations: 1 Byte = charUsed representations: 1 Byte = charUsed representations: 1 Byte = charUsed representations: 1 Byte = char2 Bytes = short2 Bytes = short2 Bytes = short2 Bytes = short4 Bytes = 4 Bytes = 4 Bytes = 4 Bytes = intintintint, long, long, long, long8 Bytes = long 8 Bytes = long 8 Bytes = long 8 Bytes = long longlonglonglong,,,,

= type identification= type identification= type identification= type identification


8 Bytes = long 8 Bytes = long 8 Bytes = long 8 Bytes = long longlonglonglong,,,,long long long long (64bit systems)(64bit systems)(64bit systems)(64bit systems)

(beside other names for the type identification)


c) Each number representation is unique, including



c) Each number representation is unique, includingthe zero (= 0)

d) The representation supports mathematical (+, -, *, /, …) and logical (equal, <, >, …) operations

1 0 1 1 01 0 1 1 01 0 1 1 01 0 1 1 0+ 1 1 1+ 1 1 1+ 1 1 1+ 1 1 1

= 1 1 1 0 1= 1 1 1 0 1= 1 1 1 0 1= 1 1 1 0 111 Carry over

2 2 2 2 2 2 2 2 decdecdecdec

+ 7 + 7 + 7 + 7 decdecdecdec

= 2 9 = 2 9 = 2 9 = 2 9 decdecdecdec


= 1 1 1 0 1= 1 1 1 0 1= 1 1 1 0 1= 1 1 1 0 1

1 0 1 1 0 1 1 0 1 1 0 1 1 0 1 1 0 1 1 0 1 1 0 1 1111 1111Value of the number Value of the number>>>>

= 2 9 = 2 9 = 2 9 = 2 9 decdecdecdec


d) cont.



d) cont.But attention:

1 1 1 1 1 1 1 11 1 1 1 1 1 1 11 1 1 1 1 1 1 11 1 1 1 1 1 1 1+ 1+ 1+ 1+ 1

1 0 0 0 0 0 0 0 01 0 0 0 0 0 0 0 01 0 0 0 0 0 0 0 01 0 0 0 0 0 0 0 0Carry over11111111

2 5 5 2 5 5 2 5 5 2 5 5 decdecdecdec

+ 1 + 1 + 1 + 1 decdecdecdec

= 0 = 0 = 0 = 0


1 0 0 0 0 0 0 0 01 0 0 0 0 0 0 0 01 0 0 0 0 0 0 0 01 0 0 0 0 0 0 0 0 = 0 = 0 = 0 = 0 decdecdecdec

aaaand not:nd not:nd not:nd not:2 5 6 2 5 6 2 5 6 2 5 6 decdecdecdec

(in a one byte addition)(in a one byte addition)(in a one byte addition)(in a one byte addition)


e) Fractional parts of a number can be represented, e.g. using a point notation






e) cont.





e) cont.



e) cont.

Used representations: 4 Byte = floatUsed representations: 4 Byte = floatUsed representations: 4 Byte = floatUsed representations: 4 Byte = float8 Bytes = double8 Bytes = double8 Bytes = double8 Bytes = double

16 Bytes = long double16 Bytes = long double16 Bytes = long double16 Bytes = long double

= type identification= type identification= type identification= type identification


(beside other names for the type identification)


f) Positive and negative numbers can be represented(absolute value sign)



(absolute value sign)

…………1 1 1 0 0 0 1 1 = 1 1 1 0 0 0 1 1 = 1 1 1 0 0 0 1 1 = 1 1 1 0 0 0 1 1 = ----99999999decdecdecdec

1 0 0 0 0 0 0 1 = 1 0 0 0 0 0 0 1 = 1 0 0 0 0 0 0 1 = 1 0 0 0 0 0 0 1 = ---- 1111decdecdecdec

1 0 0 0 0 0 0 0 = 1 0 0 0 0 0 0 0 = 1 0 0 0 0 0 0 0 = 1 0 0 0 0 0 0 0 = ---- 0000decdecdecdec

0 0 0 0 0 0 0 0 = 00 0 0 0 0 0 0 0 = 00 0 0 0 0 0 0 0 = 00 0 0 0 0 0 0 0 = 0decdecdecdec

0 0 0 0 0 0 0 1 = 10 0 0 0 0 0 0 1 = 10 0 0 0 0 0 0 1 = 10 0 0 0 0 0 0 1 = 1decdecdecdec

Not soNot soNot soNot soidealidealidealideal


0 0 0 0 0 0 0 1 = 10 0 0 0 0 0 0 1 = 10 0 0 0 0 0 0 1 = 10 0 0 0 0 0 0 1 = 1decdecdecdec

0 1 0 0 0 1 0 0 = 680 1 0 0 0 1 0 0 = 680 1 0 0 0 1 0 0 = 680 1 0 0 0 1 0 0 = 68decdecdecdec

…………

= sign= sign= sign= sign


f) cont.



f) cont.Two's complement

…………1 0 0 1 1 1 0 1 = 1 0 0 1 1 1 0 1 = 1 0 0 1 1 1 0 1 = 1 0 0 1 1 1 0 1 = ----99999999decdecdecdec

1 1 1 1 1 1 1 0 = 1 1 1 1 1 1 1 0 = 1 1 1 1 1 1 1 0 = 1 1 1 1 1 1 1 0 = ---- 2222decdecdecdec

1 1 1 1 1 1 1 1 = 1 1 1 1 1 1 1 1 = 1 1 1 1 1 1 1 1 = 1 1 1 1 1 1 1 1 = ---- 1111decdecdecdec

0 0 0 0 0 0 0 0 = 00 0 0 0 0 0 0 0 = 00 0 0 0 0 0 0 0 = 00 0 0 0 0 0 0 0 = 0decdecdecdec

0 0 0 0 0 0 0 1 = 10 0 0 0 0 0 0 1 = 10 0 0 0 0 0 0 1 = 10 0 0 0 0 0 0 1 = 1

256dec – numberdec

� convert to binary


0 0 0 0 0 0 0 0 = 00 0 0 0 0 0 0 0 = 00 0 0 0 0 0 0 0 = 00 0 0 0 0 0 0 0 = 0decdecdecdec

0 0 0 0 0 0 0 1 = 10 0 0 0 0 0 0 1 = 10 0 0 0 0 0 0 1 = 10 0 0 0 0 0 0 1 = 1decdecdecdec

0 1 0 0 0 1 0 0 = 680 1 0 0 0 1 0 0 = 680 1 0 0 0 1 0 0 = 680 1 0 0 0 1 0 0 = 68decdecdecdec

…………�� ----128128128128decdecdecdec –––– 127127127127decdecdecdec

(with a sign)(with a sign)(with a sign)(with a sign)= sign= sign= sign= sign


Octal: 8-digits

Other numeral systems:Other numeral systems:Other numeral systems:Other numeral systems:


Octal: 8-digits

Hexadecimal: 16 digits

0, 1, 2, 3, 4, 5, 6, 7, 80, 1, 2, 3, 4, 5, 6, 7, 80, 1, 2, 3, 4, 5, 6, 7, 80, 1, 2, 3, 4, 5, 6, 7, 8

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F

323323323323octoctoctocte.g.e.g.e.g.e.g.


0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F

D3D3D3D3hexhexhexhex

ByteByteByteByte

e.g.e.g.e.g.e.g.


Questions

How many bytes are needed to represent the decimal number 1024?

Which decimal number is given by

Section1-Page22

Which decimal number is given by the binary representation 11010011 (show calculation)?





implementation

Section1-Page23



A rule set for the operations

A Boolean algebraBoolean algebraBoolean algebraBoolean algebra is a set A, supplied with two elements 0 (called zero) and 1 (called one) and at least one binary operation (AND or OR) and an unary operation (NOT) as basic arithmetic operations, such that, for all elements a, boperation (NOT) as basic arithmetic operations, such that, for all elements a, band c of set A, the following axioms hold:

Section1-Page24http://en.wikipedia.org/wiki/Boolean_algebra, 2013-10-20http://de.wikipedia.org/wiki/Boolesche_Algebra, 2013-10-20





implementation

Section1-Page25



A (mechanical/electronic) electronically implementation

Out QIn A

AND , In A

In BOut Q

&In A In B Out Q

0 0 0

Rectangular shape

OR , +

Out QIn A

In B

Out QIn A In B

In A

In BOut Q

>1

In A

In B

Out Q

In B &

In A

In B

Out Q

0 0 0

0 1 0

1 0 0

1 1 1

In A In B Out Q

0 0 0

0 1 1

1 0 1

1 1 1

Distinctive shape

Section1-Page26

Out QIn A In AInductor

In B

In A Out Q1

In A Out Q

Out QIn A

NOT A ,

1 1 1

In A Out Q

0 1

1 0


Design of new gate combinations


Building of the Disjunctive Normal Form (DNF)In A In B Out Q

0 0 1 A AND B

0 1 1 A AND B

1 0 0

1 1 1 A AND B

e.g.( ) OR

= Out

Building of the Disjunctive Normal Form (DNF)

( ) OR

( )

&>1

A B

Section1-Page27http://edascript.ims.uni-hannover.de/230b_Logikoptimierung/fla/Logikoptimierung.swf, 2013-10-20

>1

&

&

>1Out


Simplification of logic gates (= reduction of the number of gates)


Q = ( A AND B ) OR ( A AND B ) OR ( A AND B )Disjunctive normal form

Mathematical formal solution Graphical solution

Q = ( A AND B ) OR ( A AND B ) OR ( A AND B )

= ( A AND B ) OR ( A OR A ) AND B

= ( A AND B ) OR 1 AND B

distributivity

complements

boundedness

Quine-McClusky-Algorithm Karnaugh-Veitch-diagram

A A

B 1 1 B

A AND B A AND B

Section1-Page28

Q = ( A OR B )

= ( A AND B ) OR B

= ( B OR A ) AND ( B OR B)

= ( B OR A ) AND 1

= ( B OR A )

distributivity

complements

boundedness

http://edascript.ims.uni-hannover.de/230b_Logikoptimierung/fla/Logikoptimierung.swf, 2013-10-20

B 0 1 A

A AND B A AND B


Simplification of logic gates (= reduction of the number of gates)


Q = ( A AND B ) OR Q = ( A OR B )Q = ( A AND B ) OR ( A AND B ) OR ( A AND B )

Q = ( A OR B )

&>1

&>1

A B

Out>1

A B

Out

Simplification


&

>1 >1

3 AND gates2 OR gates3 NOT gates

Σ: 8 gates

0 AND gates1 OR gates1 NOT gates

Σ: 2 gates



- Combine groups with 16, 8, 4, 2, 1 elements

Karnaugh-Veitch-diagramGraphical solution, which results in the optimal minimum for the number of gates

- Combine groups with 16, 8, 4, 2, 1 elementsto one block

- Create always blocks with a maximumnumber of elements

- Write down all contributing elements to a block and cancel those, which contribute in a negated and not negated way

- The elements can be used multiply- The edges of the diagram continue at the

A A

B 1 1

B 0 1 A

B

A AND B

A AND B

A AND B

A AND B

Section1-Page30

1 1


- The edges of the diagram continue at theother end, so that crossing is allowed

A AND B A AND B



Karnaugh-Veitch-diagram

With three inputs A, B and C With four inputs A, B, C and D

A

B 1 1

B 1 0

BA A

1 1

0 1

1 1

1 1

1 1

0 1

0 1

0 0

D

AA A

B

B

A AND D

Section1-Page31


B 1 0

A

0 1

C C

1 1

1 1

0 0

0 0

C C

D

B

C


Cross checking for correctness


Source table: Karnaugh-Veitch-diagram:

Check simplification:

A B C D NOT D ((NOT A) C OUT =

A B C D OUT0 0 0 0 00 0 0 1 10 0 1 0 10 0 1 1 10 1 0 0 00 1 0 1 10 1 1 0 10 1 1 1 11 0 0 0 0

diagram: A B C D NOT A

D ((NOT A) AND D)

C OUT =C OR

((NOT A) AND D)

0 0 0 0 1 0 0 0 00 0 0 1 1 1 1 0 10 0 1 0 1 0 0 1 10 0 1 1 1 1 1 1 10 1 0 0 1 0 0 0 00 1 0 1 1 1 1 0 10 1 1 0 1 0 0 1 10 1 1 1 1 1 1 1 11 0 0 0 0 0 0 0 0


1 0 0 0 01 0 0 1 01 0 1 0 11 0 1 1 11 1 0 0 01 1 0 1 01 1 1 0 11 1 1 1 1

equal?equal?equal?equal?

1 0 0 0 0 0 0 0 01 0 0 1 0 1 0 0 01 0 1 0 0 0 0 1 11 0 1 1 0 1 0 1 11 1 0 0 0 0 0 0 01 1 0 1 0 1 0 0 01 1 1 0 0 0 0 1 11 1 1 1 0 1 0 1 1


Half-

Realization of a calculation machine (adder)


Building of the Half-Adder

(addition of two bits resulting in a sum and a carry-out bit)

In A In B Sum S

0 0 0

0 1 1

1 0 1

1 1 0

In A In B C out

0 0 0

0 1 0

1 0 0

A AND B( ) OR= S

= C

A AND B( )


A AND B( )

&

&

&

>1 Sum S

Carry Cout

XOR

=1In AIn B

Section1-Page33

1 1 1 = CoutA AND B( ) &

In A

In B HA

Sum S

Carry Cout

But to add one Byte (= 8 bits) it is also necessary to add the But to add one Byte (= 8 bits) it is also necessary to add the But to add one Byte (= 8 bits) it is also necessary to add the But to add one Byte (= 8 bits) it is also necessary to add the carrycarrycarrycarry----out from the previous bit. out from the previous bit. out from the previous bit. out from the previous bit.


Full-

In A In B Sum S

0 0 0 0

Cin




Full-Adder

(addition of two bits and an additional carry-in bit resulting in a sum and a

0 0 0 0

0 0 1 1

0 1 0 1

0 1 1 0

1 0 0 1

1 0 1 0

1 1 0 0

1 1 1 1

In A In B Cout

0 0 0 0

Cin

Cin AND A AND B

Cin AND A AND B

Cin AND A AND B

Cin AND A AND B

( ) OR

( ) OR

( ) OR

( )

= S

Section1-Page34

and a carry-out bit)

0 0 1 0

0 1 0 0

0 1 1 1

1 0 0 0

1 0 1 1

1 1 0 1

1 1 1 1

Cin AND A AND B

Cin AND A AND B

Cin AND A AND B

Cin AND A AND B

( ) OR

( ) OR

( ) OR

( )

= Cout


&

Cin A B



Full-Cin AND A AND B

Cin AND A AND B

Cin AND A AND B

Cin AND A AND B

( ) OR

( ) OR

( ) OR

( )

= S

>1

&

>1&

&&

&&

&&

>1S

Cin A B

Full-Adder


Section1-Page35

Cin AND A AND B

Cin AND A AND B

Cin AND A AND B

Cin AND A AND B

( ) OR

( ) OR

( ) OR

( )

= Cout

>1

&

>1&

&&

&&

&&

>1Cout





Full- or as realization with two half addersFull-Adder


&

=1

>1HA

&

=1

HA

Sum S

CarryOut CIn A

In B

Carry In C

or as realization with two half adders

Section1-Page36


In A

FA

Sum S

Carry Out C Carry In C

In B




Full- Addition of 8 bits (= 1 Byte)Full-Adder


FA

S0

Cout Cin

A0 B0

FA

S1

Cout Cin

A1 B1

FA

S2

Cout Cin

A2 B2

FA

S3

Cout Cin

A3 B3

FA

S4

Cout Cin

A4 B4

FA

S5

Cout Cin

A5 B5

FA

S6

Cout Cin

A6 B6

FA

S7

Cout Cin

A7 B7

Addition of 8 bits (= 1 Byte)

Section1-Page37



Memory gates: flip-flops


Set Reset Out Qt+1RS-Flipflop &S Q

S Q1S0 0 -

0 1 0

1 0 1

1 1 Qt

RS-Flipflop

&RQ

R

S

Q

Q

1R

1S

J K Out Qt+1

0 0 Qt

0 1 0

1 0 1

1 1 Q

Triggered JK-Master-Slave-Flipflop

Q

K

J

Q

Section1-Page38

1 1 Qt

http://upload.wikimedia.org/wikipedia/commons/f/f5/ISO-JK-FF-NAND-circuit.svg, 2013-10-20


The modern logic gates: from valves to wafer circuits


„A transistortransistortransistortransistor is a semiconductor device, commonly used as an amplifier

„In electronics, a vacuumtube, electron tube (insideNorth America),

„In electronics, an integrated integrated integrated integrated circuitcircuitcircuitcircuit (also known as IC, microcircuit, microchip, silicon

„In microelectronics, a wafer is a thin slice of semiconducting material, such as a silicon crystal, upon which

Section1-Page39

commonly used as an amplifier or an electrically controlled switch. The transistor is the fundamental building block of the circuitry (intecrated circuits) that governs the operation of computers and all other modern electronics.“

North America), thermionic valve, or just valvevalvevalvevalve (elsewhere); is a device used to amplify, switch, otherwise modify, or create an electricalsignal by controlling themovement of electrons in a low-pressure space.“

microcircuit, microchip, silicon chip, or chip) is a miniaturized electronic circuits (consisting mainly of semiconductor device, as well as passive components) that has been manufactured in the surface of a thin substrate of semiconductor material.“

such as a silicon crystal, upon which microcircuits are constructed by doping (for example, diffusion or ion implantation), chemical edging, and deposition of various materials. Wafers are thus of key importance in the fabrication of semiconductor devices such as integrated circuits.“

http://en.wikipedia.org/wiki/Vacuum_tube, 2007.09.02http://en.wikipedia.org/wiki/Transistor, 2007.09.02http://en.wikipedia.org/wiki/Integrated_circuits, 2007.09.02http://en.wikipedia.org/wiki/Wafer_%28electronics%29, 2007.09.02


Questions

Simplify the following truth table (define your used signs/ pictograms for AND, OR, NOT and use disjunctive normal form; advice for final test: task type could be similar with changed truth table values)test: task type could be similar with changed truth table values)

A B C D OUT0 0 0 0 00 0 0 1 10 0 1 0 00 0 1 1 00 1 0 0 00 1 0 1 00 1 1 0 10 1 1 1 1

Use a Karnaugh-Veitch-diagram

Use the mathematical method given by the axioms of Boolean algebra

Section1-Page40

0 1 1 1 11 0 0 0 01 0 0 1 11 0 1 0 01 0 1 1 01 1 0 0 01 1 0 1 01 1 1 0 11 1 1 1 1

Draw the logic gate map for simplified table (define the used graphical symbols in a short caption)





implementation

Section1-Page41




The heart of a computer: the central processing unit (CPU) or processor

Input Output

Main memory

ArithmeticLogic

ControlUnit

CPU


John von Neumann –Architecture (1945)

LogicUnit

Unit



The heart of a computer: the central processing unit (CPU) or processor

Input/output: used to commit data and programs to the memory

Main memory:stores data and programs, to offer them to the CPU

Control unit:stores the current instruction (in registers), counts them,


stores the current instruction (in registers), counts them, and decodes them to control the ALU

Arithmetic Logic Unit (ALU):processes mathematical and logical operations, controlled by the control unit

Lecture 1: Computer architecture

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