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Chapter4: Combinational Logic
Part 4Originally By Reham S. Al-Majed
Imam Muhammad Bin Saud University
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Outline
2
Multiplexer
DefinitionExamplesMUX and Decoder.MUX Expansion.Circuit Implementation with MUX
DeMultiplexer
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Definition
3
It is a cc that select binary information from one of many inputlines to single output line.
The selection of input line depends on selection lines.
Its ab consists of:Inputs lines = 2 n
Output line = 1Selectors (depends on number of inputs) = nAn active high or active low enable input (not all multiplexers have it)
I2n
-1
I0
MUX....
S0
Sn-1
2n Inputs lines
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Definition
4
I0
I1
I2
I3
00
MUX Y=I 0
I0
I1
I2
I3
10
MUX Y=I 1
I0
I1
I2I3
01
MUXY= I
2
I0
I1
I2
I3
11
MUX Y=I 3
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Example 1
5
Design a 2-to-1 multiplexer:1. 2 data inputs (I 0,I1), 1 select input S , and 1 output (Y)2. Truth table:
S I 1 I 0 Y0 0 0 I 0=0
0 0 1 I 0=1
0 1 0 I 0=0
0 1 1 I 0=1
1 0 0 I 1=0
1 0 1 I 1=0
1 1 0 I 1=1
1 1 1 I 1=1
S Y
0 I0
1 I1
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Example 1 (cont.)
6
3. Simplification:
Y = S’ I 0 + S I 1
3. Diagram:
1 1
1 1S
I 0
I1
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Example 2
7
Design 4-to1 MUX:
There are four data inputs two selection inputs S 1,S0.The input selected to be passed to the output depends on the minterm ofthe input.
Y = S 1 ’S 0 ’I0 + S 1 ’S 0 I 1 + S 1 S 0 ’I2 + S 1 S 0 I 3
minterm S 1 S0 Ym0 0 0 I0
m1 0 1 I1
m2 1 0 I2
m3 1 1 I3
m1 m2 m3m0
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Multiplexer and Decoder
8
The AND gates and inverters in the MUX resemble a decoder
circuit.
They decode selection input lines.
2n-to-1 line multiplexer is constructed from n-to-2 n decoder.
Example:
4-to-1 MUX constructed from 2-to-4 decoder
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Multiplexer Expansion
9
Design a 4-to-1 MUX with 2-to-1 MUXes only.4-to-1 has 4 data input, 2 selection input, and 1 output.2-to-1 has 2 data input, 1 selection input, and 1 output.
S1 S0 Y
0 0 D0
0 1 D1
1 0 D2
1 1 D3
D0
D1
MUX
MUX
D2
D3
MUX
•
Y
S0S1
I0
I1
I 0
I 1
I 0
I 1
•
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CC Implementation with MUX
10
Given a function of n-variables MUXex can be used to implement this
function.
This can be accomplished in one of 2 ways:Using a Mux with n-select inputs
n variables need to be connected to n select inputs.Minterms of a function are generated according to select inputs.Individual minterm can be selected by the data inputs proper assignment of the datainputs (D i ∈ {0 , 1}).
Using a Mux with n-1 select inputs (more efficient)Find truth table.The first n-1 variables in table are connected to selection inputs of MUX (which order?).For each combination of selection variables, evaluate output as function of theremaining variable (d)This remaining variable (d) is then used for data inputs which can be 0,1 ,d,d’.
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Example 1
11
Implement the function F(x,y,z ) = ∑( 1,2,6,7) using a Mux with n-
select inputs.
The function has 3 variables using 3-select inputs, we need a 8-to-1 MUX.
8-to-1MUX
x y z
F
1
0
1
1
1
0
0
0
1
0
2 3
4
5
6 7
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De-Multiplexer
13
It is a CC that performs the inverse operation of MUX.
It has:
1 input2n outputs.
n selection inputs to select outputs.
Example: design 1-to-4 DeMUX
1-to-4DeMUX
A1
E
A0
D0
D1
D2
D3
A1 A0 D0 D1 D2 D3
0 0 E 0 0 0
0 1 0 E 0 0
1 0 0 0 E 0
1 1 0 0 0 E
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Reading
14
4.1
4.2
4.3
4.4
4.5EXCEPT: Carry propagation.
4.6 Reading Assignment.
4.7 Reading Assignment.
4.9
4.10
4.11