DIGITAL LOGIC DESIGN
by
Dr. Fenghui Yao
Tennessee State University
Department of Computer Science
Nashville, TN
Combinational Logic
1
Remember
Inputs
.
.
.

Network
.
Outputs
.
Combinational



.
The outputs depend only on the current input
values
It uses only logic gates
Sequential


The outputs depend on the current and past input
values
It uses logic gates and storage elements
Combinational Logic
2
Notes



If there are n input variables, there are
2^n input combinations
For each input combination, there is
one output value
Truth tables are used to list all possible
combinations of inputs and
corresponding output values
Combinational Logic
3
Basic Combinational
Circuits
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Adders
Multipliers
Multiplexers
Decoders
Encoders
Comparators
Subtractors
Combinational Logic
4
Design

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Determine the inputs and outputs
Assign a symbol for each
Derive the truth table
Get the simplified boolean expression
for each output
Draw the network diagram
Combinational Logic
5
Example

Conversion from BCD to excess-5
Combinational Logic
6
Example (Cont.)
W  A  B  CD
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7
Example (Cont.)
X  A  B' D'B' C'BCD
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8
Example (Cont.)
Find Y and Z
Draw the network diagram
Combinational Logic
9
Adders


Essential part of every CPU
Half adder (Ignore the carry-in bit)


It performs the addition of two bits
Full adder

It performs the addition of three bits
Combinational Logic
10
Half-Adder


You can use K-Map to simplify
It is also obvious from the truth table
Combinational Logic
11
Full-Adder
Combinational Logic
12
Full-Adder
Si  Ai  Bi  Ci
Ci 1  Ai Bi ' Ci  Ai ' Bi Ci  Ai Bi
Combinational Logic
HOW?????
13
4-bit Adder Implementation
From course book
C0  0
Combinational Logic
14
Question

How can you get 32-bit implementation?
Combinational Logic
15
Binary Subtractor

Remember


You need to take 2’s complement to represent
negative numbers
A-B

Take 2’s complement of B and add it to A

Combinational Logic
First take 1’s complement and add 1
16
4-Bit Adder and Subtractor
From course book
Combinational Logic
M  0( Adder )
M  1( Subtractor )
V (Overflow)
17
Binary Multiplier
Combinational Logic
From course book
18
Comparators

Compare two input words

Combinational Logic
Returns 1 if
A=B, 0
otherwise
19
Combinational Logic
From course book
20
Decoder

n by 2^n decoder



Converts information from n input lines into 2^n
output lines
2x4 Decoder
3x8 Decoder
Combinational Logic
21
2x4 Decoder
Combinational Logic
22
Internal Structure of 2x4
Decoder
Combinational Logic
23
Another View
Combinational Logic
24
From
course
book
Combinational Logic
25
Example
Combinational Logic
26
4x16 Decoder
From course book
Combinational Logic
27
Full Adder with Decoder
Si  Ai  Bi  Ci
Ci 1  Ai Bi ' Ci  Ai ' Bi Ci  Ai Bi
Combinational Logic
28
Multiplexers



You can select information from one of
many input lines and assign it to one
output line
You have input lines, control lines, and
one output line
It is called MUX
Combinational Logic
29
2x1 Multiplexer
Combinational Logic
30
4x1 Multiplexer
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31
Boolean Function
Implementation
How do you implement it with 8x1 MUX?
Combinational Logic
32
Example
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33
Three-State Buffer
Combinational Logic
34
2x1 MUX with Three-State
Buffer
Combinational Logic
35
Shifters
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
8-input, 8-output shifter
C=1 => right shift, C=0 => left shift
Combinational Logic
36
Study Problem

Course Book Chapter – 4 Problems

4 – 31

Combinational Logic
Construct a 16x1 multiplexer with two 8x1 and
one 2x1 multiplexer. Use block diagrams
37
Study Problem

Course Book Chapter – 4 Problems

4 – 34
An 8x1 multiplexe r has inputs A, B, and C connected to
the selection inputs S2 , S1 , and S0 respective ly.
The data inputs
I1  I 2  I 7  0;
I 3  I 5  1;
I 0  I 4  D;
I 6  D'
Determine the Boolean function t hat the multiplexe r implements
Combinational Logic
38
Study Problems

Course Book Chapter – 4 Problems
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4–1
4–4
4–6
4 – 11
4 – 20
4 – 21
4 – 25
4 – 32
4 – 33
4 – 35
Combinational Logic
39
Questions
Combinational Logic
40