The architecture of computer hardware and systems software an information technology approach suplement 1

SUPLEMENTARY CHAPTER 1:An Introduction to Digital Logic The Architecture of Computer Hardware and Systems Software: An Information Technology Approach 3rd Edition, Irv Englander John

SUPLEMENTARY CHAPTER 1:

An Introduction to Digital Logic

The Architecture of Computer Hardware

and Systems Software:

An Information Technology Approach

3rd Edition, Irv Englander John Wiley and Sons 2003

Integrated Circuits

 The building blocks of computers

 Designed for specialized functions

 Examples: the CPU, bus interface,

memory management unit

 Transistors : primary components of ICs

 Motorola MPC 7400 PowerPC modules: 6.5 million transistors in less than ½ in2

 Boolean algebra : basis for computer logic design

 Transistors: means for implementing Boolean algebra

 Switches: on/off to represent the 0’s and 1’s of binary digital circuits

 Combined to form logic gates

Digital Circuits

 Combinatorial logic

 Results of an operation depend only on the

present inputs to the operation

 Uses: perform arithmetic, control data movement, compare values for decision making

 Sequential logic

 Results depend on both the inputs to the operation

and the result of the previous operation

 Uses: counter

Boolean Algebra

 Rules that govern constants and variables that can take on 2 values

 True/false; on/off; yes/no; 0/1

 Boolean logic

 Rules for handling Boolean constants and

variables

 3 fundamental operations:

AND , OR and NOT

 Truth Table: specifies results for all possible input combinations

Boolean Operators

 AND

 Result TRUE if and only if both

input operands are true

 C = A  B

 INCLUSIVE-OR

 Result TRUE if any input operands

are true

 C = A + B

0 0 0

0 1 0

1 0 0

1 1 1

0 0 0

0 1 1

1 0 1

1 1 1

Boolean Operators

 NOT

 Result TRUE if single input value is

FALSE

 C = A

A C

0 1

1 0

Boolean Operators

 Result TRUE if either A or B is

TRUE but not both

 C = A ⊕ B

 Can be derived from

INCLUSIVE-OR, AND and NOT



A xor B equals A or B but not both A and B



A xor B = either A and not B or B and not A

0 0 0

0 1 1

1 0 1

1 1 0

A ⊕ B = (A + B)  ( A  B )

A ⊕ B = (A  B ) + ( B  A )

Boolean Algebra Operations

 Valid for INCLUSIVE-OR, AND, XOR

 Associative



 Distributive



 Commutative



 DeMorgan’s Theorems



A + ( B + C ) = ( A + B ) + C

A  ( B + C ) = A  B + A  C

A + B = B + A

A + B = A  B

Gates and Combinatorial Logic

 Many computer functions defined in terms of Boolean equations

 Example: sum of 2 single binary digit numbers

 Truth table for sum Truth table for carry

0 0 0

0 1 0

1 0 0

1 1 1

0 0 0

0 1 1

1 0 1

1 1 0

Computer Implementation

 Gates or logical gates

 Integrated circuits constructed from transistor switches and other electronic components

 VLSI : very large-scale integration

Boolean Algebra

Implementation

 Single type of gate appropriately combined

 2 possibilities

 NAND gate: AND operation followed by a NOT operation

 NOR gate: INCLUSIVE-OR followed by a NOT operation

Note:  indicates a NOT operation

Selector or Multiplexer

 Switch input back and forth between inputs

 Logic circuits that make up a computer

 are relatively simple but

 look complicated because many circuits required

Half-Adder

Full Adder

 Handles possible carry from previous bit

 Half adder shown as block to simplify

(portion of half adder in Fig S1.11 enclosed in dotted line)

 2-bit adder contains 32 circuits

 Also called ripple adder because the carry

Sequential Logic Circuits

 Output depends on

 Input

 Previous state of the

circuit

 Flip-flop : basic memory

element

 State table : output for

all combinations of input

and previous states

 Cf Truth Table

Flip-Flop Types with State Tables

Register COPY Operation

 Uses both

sequential and

combinatorial

logic

Steps in a LOAD Instruction