13. Design the 32:1 multiplexer using 4:1 multiplexer tree concept
and implement the function F = {0, 1, 3, 8, 9, 13) using suitable
multiplexer.
For 32:1 multiplexer,
no. of inputs = 32(L, I, I.......... 131)
no. of outputs = 1
no. of selection lines = 5(S., S3, S2, S., S) -
For 4:1 multiplexer,
no. of inputs = 4(1, 11, 12, 13)
Answers
Answer:
Explanation:
The chemicals that undergo chemical change in a
chemical reaction are called reactants.
Answer:
we assume that we have one-bit inputs
(in general, each input may have more than one bit)
• Suppose we have eight inputs: I0, I1, I2, I3, I4, I5, I6, I7
• We want one of them to be output based on selection signals
• 3 bits of selection signals to decide which input goes to output
• Note the order of selection signals
– X is MSB and Z is LSB
Multiplexing and Multiplexer
X Y Z F
0 0 0 I0
0 0 1 I1
0 1 0 I2
0 1 1 I3
1 0 0 I4
1 0 1 I5
1 1 0 I6
1 1 1 I7
S2
S1
S0 F
0 1 2 3 4 5 6 7
I0 I1 I2 I3 I4 I5 I6 I7
X
Y
Z
8-to-1 Multiplexer
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• We can write a logic expression for output F as follows
F = X’ Y’ Z’ I0 + X’ Y’ Z I1 + X’ Y Z’ I2 + X’ Y Z I3
+ X Y’ Z’ I4 + X Y’ Z I5 + X Y Z’ I6 + X Y Z I7
• This circuit can be implemented using
– eight 4-input AND gates and one 8-input OR gates
Multiplexer Implementation
S2
S1
S0 F
0 1 2 3 4 5 6 7
I0 I1 I2 I3 I4 I5 I6 I7
X
Y
Z
X Y Z F
0 0 0 I0
0 0 1 I1
0 1 0 I2
0 1 1 I3
1 0 0 I4
1 0 1 I5
1 1 0 I6
1 1 1 I7
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Implementing 4-to-1 MUX using 2-to-1 MUXs
S0 2x1 MUX
0 1
I0 I1
S0 S0 2x1 MUX
0 1
I2 I3
S0
S0 2x1 MUX
0 1 S1
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Making a 2-bit 4-to-1 Multiplexer
X
Y F
0 1 2 3
4-1 S1 MUX
S0
X
Y F
0 1 2 3
4-1 S1 MUX
S0
X
Y
ABCD
• Four 2-bit inputs A, B, C, D
• One 2-bit output F
• Two bits of selection signal X Y
F
X Y F
0 0 A
0 1 B
1 0 C
1 1 D
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• Multiplexers can be directly used to implement a function
• Easiest way is to use function inputs as selection signals
• Input to multiplexer is a set of 1s and 0s depending on the
function to be implemented
• We use a 8-to-1 multiplexer to implement function F
• Three select signals are X, Y, and Z, and output is F
• Eight inputs to multiplexer are 1 0 1 0 1 1 0 0
• Depending on the input signals
– multiplexer will select proper output
Synthesis of Logic Functions using Multiplexers
X Y Z F
0 0 0 1
0 0 1 0
0 1 0 1
0 1 1 0
1 0 0 1
1 0 1 1
1 1 0 0
1 1 1 0
S2
S1
S0 F
X 0 1 2 3 4 5 6 7
Y
Z
10101100
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