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 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

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Digital Computer Logic

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Transistors
 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

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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

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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
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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

Supplementary Chapter 1
Digital Computer Logic

A

B

C

0

0

0

0

1

0

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0

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1

1

A

B

C

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Boolean Operators
 NOT

A

C

0

1

1

0

 Result TRUE if single input value is
FALSE
 C=A

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Boolean Operators
 EXCLUSIVE-OR

 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 ⊕ B = (A + B)  ( A  B )
A xor B equals A or B but not both A and B
A ⊕ B = (A  B ) + ( B  A )
A xor B = either A and not B or B and not A

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A

B

C

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Boolean Algebra Operations
 Valid for INCLUSIVE-OR, AND, XOR
 Associative


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

 Distributive


A  ( B + C ) = A  B +A  C

 Commutative


A + B =B + A

 DeMorgan’s Theorems


A + B =A  B



A  B =A + B

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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
XOR
AND

A

B

C

A

B

C

0

0

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0

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Computer Implementation
 Gates or logical gates
 Integrated circuits constructed from transistor
switches and other electronic components
 VLSI: very large-scale integration

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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
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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

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Half-Adder

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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

ripples through 32 bits
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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

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Flip-Flop Types with State Tables

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Register COPY Operation
 Uses both
sequential and
combinatorial
logic

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Steps in a LOAD Instruction

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