suplementary chapter 1: an introduction to digital logic the architecture of computer hardware and...
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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
Linda Senne, Bentley College
Wilson Wong, Bentley College
Supplementary Chapter 1 Digital Computer Logic
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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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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
A B C
0 0 0
0 1 0
1 0 0
1 1 1
A B C
0 0 0
0 1 1
1 0 1
1 1 1
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Boolean Operators
NOT Result TRUE if single input value is
FALSE C = A
A C
0 1
1 0
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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 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
A B C
0 0 0
0 1 1
1 0 1
1 1 0
A ⊕ B = (A + B) ( A B )
A ⊕ B = (A B ) + ( B A )
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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
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
0 0 0
0 1 0
1 0 0
1 1 1
A B C
0 0 0
0 1 1
1 0 1
1 1 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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Copyright 2003 John Wiley & Sons
All rights reserved. Reproduction or translation of this work beyond that permitted in Section 117 of the 1976 United States Copyright Act without express permission of the copyright owner is unlawful. Request for further information should be addressed to the permissions Department, John Wiley & Songs, Inc. The purchaser may make back-up copies for his/her own use only and not for distribution or resale. The Publisher assumes no responsibility for errors, omissions, or damages caused by the use of these programs or from the use of the information contained herein.