Encoders, DeMUXs & MUXs. Outline Encoder Demultiplexer Multiplexer Multiplexer IC Package.
Multiplexer MUX. 2 Multiplexer Multiplexer (Selector) 2 n data inputs, n control inputs, 1 output...
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Transcript of Multiplexer MUX. 2 Multiplexer Multiplexer (Selector) 2 n data inputs, n control inputs, 1 output...
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Multiplexer
• Multiplexer (Selector) 2n data inputs, n control inputs, 1 output
Used to connect 2n points to a single point
control signal pattern form binary index of input connected to output
2:1 mux
I 0
I 1
A
Z
I 0
A
I 1 I 2 I 3
B
Z 4:1 mux
I 0
A
I 1 I 2 I 3
B
Z 8:1
mux
C
I 4 I 5 I 6
I 7
A 0 1
Z I 0 I 1
4
Boolean FunctionsZ = A' I0 + A I1
Z = A' B' I0 + A' B I1 + A B' I2 + A B I3
Z = A' B' C' I0 + A' B' C I1 + A' B C' I2 + A' B C I3 + A B' C' I4 + A B' C I5 + A B C' I6 + A B C I7
2:1 mux
I 0
I 1
A
Z
I 0
A
I 1 I 2 I 3
B
Z 4:1 mux
I 0
A
I 1 I 2 I 3
B
Z 8:1
mux
C
I 4 I 5 I 6
I 7 In general, Z = mk Ik
in minterm shorthand form
2n -1
k=0
A I0 A
I0
I1 00 01 11 10
0
1
0
0
1
1
0
1
0
1
6
Cascading MUXes
Design a MUX (8:1) by smaller MUXes
Z
A C B
I 0 I 1 I 2 I 3
I 4 I 5 I 6 I 7
4:1 mux
0 1 2 3 S 1 S 0
4:1 mux
0 1 2 3 S 1 S 0
2:1 mux
S
0
1
7
Another Implementation
0
1 S
0
1 S
0
1 S
0
1 S
0
1
S1
2
3 S0
C
A B
I 0
I 1
I 2
I 3
I 4
I 5
I 6
I 7
C
C
C
Z
8
Larger Data Lines
What if we want to select m-bit data/words?
Combine MUX blocks in parallel with common select and enable signals
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4-bit data
• Example: Selection between
2 sets of 4-bit inputs
Enable line turns MUX on and off (E=1 is on).
2:1 mux
I 0
I 1
A
Z
2:1 mux
I 0
I 1
A
Z
2:1 mux
I 0
I 1
A
Z
2:1 mux
I 0
I 1
Z
x0
x1
x2
x3
y0
y1
y2
y3
z0
z1
z2
z3
A
?
12
General Logic by MUX
Any Boolean function of n variables can be implemented using a 2n-1-to-1 multiplexer.
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General Logic by MUX
• Example:F = A' B' C' + A' B C' + A B C' + A B C
= A' B' (C') + A' B (C') + A B' (0) + A B (1)
A 0 0 0 0 1 1 1 1
B 0 0 1 1 0 0 1 1
C 0 1 0 1 0 1 0 1
F 1 0 1 0 0 0 1 1
C’
C’
0
1
1 0 1 0 0 0 1 1
8:1 MUX
0 1 2 3 4 5 6 7 S2 S1 S0
A B C
F
A 0 0 1 1
B 0 1 0 1
F C’ C’ 0 1
S1 S0
A B
4:1 MUX
0 1 2 3
C
C01
F
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Using Smaller MUX
How about implementing a 4-variable function by a 4-to-1 MUX− Anything else is needed?
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General Logic
• By decoder: Multiple outputs:
− A single decoder,− One more OR for each output
• By MUX: Multiple outputs:
− One more MUX for each output,− No need for OR
Use MUX for few outputs, Use decoder for many outputs.
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Decoder vs. Demux
ABC ABC ABC ABC ABC ABC
ABC ABC
3:8 dec
O0 O1
O2
A
B
C
Enb
S2
S1
S0
O3
O4
O5
O6
O7
E A B C O0 O1 O2 O3 O4 O5 O6 O7
0 X X X 0 0 0 0 0 0 0 0
1 0 0 0 1 0 0 0 0 0 0 0
1 0 0 1 0 1 0 0 0 0 0 0
1 0 1 0 0 0 1 0 0 0 0 0
1 0 1 1 0 0 0 1 0 0 0 0
1 1 0 0 0 0 0 0 1 0 0 0
1 1 0 1 0 0 0 0 0 1 0 0
1 1 1 0 0 0 0 0 0 0 1 0
1 1 1 1 0 0 0 0 0 0 0 1