Transcript SUPLEMENTARY CHAPTER 1: An Introduction to Digital Logic

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
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
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
 INCLUSIVE-OR
 Result TRUE if any input operands
are true
 C=A+B
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Boolean Operators
 NOT
 Result TRUE if single input value is
FALSE
 C=A
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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
B
C
0
0
0
0
1
1
1
0
1
1
1
0
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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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
0
0
0
0
0
1
1
0
1
0
1
0
1
1
0
0
1
1
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1
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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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