Introduction to Digital Logic
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Transcript Introduction to Digital Logic
Introduction to Digital
Logic
Modified from :
The Architecture of Computer
Hardware and Systems Software:
An Information Technology Approach
3rd Edition, Irv Englander
John Wiley and Sons 2003
Note to Students
Students usually find this topic easy (although it
looks hard at first!)
We will not do math—Boolean algebra
We will focus on the basics: LOGIC GATES
Why are we studying Digital
Logic?
Digital logic performs the basic
instructions of a processor….
ADD, SUB, JUMP, etc
These are “hard-wired” into the system.
We don’t study the components that
make up the gates – transistors,
capacitors, circuits etc..
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Little picture….
It all starts with LOGIC
The logic is implemented with electrical
devices
The individual devices are organized
together in very clever ways to perform
VERY SIMPLE functions:
Check if the 5th bit of the PSW=1?
ADD two binary numbers (integer)
Find the sign, exponent and mantissa of a
floating point number
Determine the op-code and operand of an
instruction
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Big picture….
The simple instructions of a CPU combine to form
useful work:
1) Sort all the names in a DATABASE by last name
2) Send a file to the printer
3) Network different devices together
4) Use the internet
5) Track 2 million bank accounts
6) Play music and movies
7) Take a class on-line
8) Write a book (or letter or report) and store it
electronically for later use
9) Store huge amounts of information electronically
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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 con’t
Transistors: are the 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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Boolean Logic
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
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
0
1
1
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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EXAMPLE
Example 1: Complete the truth
table for the following circuit:
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EXAMPLE
Fill-in the table:
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EXAMPLE
Fill-in the table:
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EXAMPLE
Fill-in the table:
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EXAMPLE
Fill-in the table:
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EXAMPLE
Fill-in the table:
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In Class: How to get started?
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