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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
S1-2
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
Supplementary Chapter 1 Digital Computer Logic
S1-3
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
Supplementary Chapter 1 Digital Computer Logic
S1-4
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
Supplementary Chapter 1 Digital Computer Logic
S1-5
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
Supplementary Chapter 1 Digital Computer Logic
S1-6
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
Supplementary Chapter 1 Digital Computer Logic
S1-7
Boolean Operators
NOT Result TRUE if single input value is
FALSE C = A
A C
0 1
1 0
Supplementary Chapter 1 Digital Computer Logic
S1-8
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 )
Supplementary Chapter 1 Digital Computer Logic
S1-9
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
Supplementary Chapter 1 Digital Computer Logic
S1-10
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
Supplementary Chapter 1 Digital Computer Logic
S1-11
Computer Implementation
Gates or logical gates Integrated circuits constructed from transistor
switches and other electronic components VLSI: very large-scale integration
Supplementary Chapter 1 Digital Computer Logic
S1-12
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
Supplementary Chapter 1 Digital Computer Logic
S1-13
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
Supplementary Chapter 1 Digital Computer Logic
S1-14
Half-Adder
Supplementary Chapter 1 Digital Computer Logic
S1-15
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
Supplementary Chapter 1 Digital Computer Logic
S1-16
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
Supplementary Chapter 1 Digital Computer Logic
S1-17
Flip-Flop Types with State Tables
Supplementary Chapter 1 Digital Computer Logic
S1-18
Register COPY Operation
Uses both sequential and combinatorial logic
Supplementary Chapter 1 Digital Computer Logic
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Steps in a LOAD Instruction
Supplementary Chapter 1 Digital Computer Logic
S1-20
Copyright 2003 John Wiley & Sons
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