Chapter 1: Q17E (page 2)
B.17 [5] <§§B.2, B.3> Show a truth table for a multiplexor (inputs A, B, and S; output C ), using don’t cares to simplify the table where possible .
Short Answer
The truth table for the multiplexer:
Input:A | Input:B | Input:S | Output:C |
0 | 0 | 0 | B’ |
0 | 0 | 1 | B’ |
0 | 1 | 0 | B |
0 | 1 | 1 | B |
1 | 0 | 0 | B’ |
1 | 0 | 1 | B’ |
1 | 1 | 0 | B |
1 | 1 | 1 | B |
Step by step solution
Define the concept.
The required multiplexer, where “A”,”B”,”S” is the inputs and “C” is the output by using the “don’t care”:
Determine the calculation
The required truth table for the multiplexer, where “A”,”B”,”S” is the inputs and “C” is the output by using the “don’t care”::
Input:A | Input:B | Input:S | Output:C |
0 | 0 | 0 | B’ |
0 | 0 | 1 | B’ |
0 | 1 | 0 | B |
0 | 1 | 1 | B |
1 | 0 | 0 | B’ |
1 | 0 | 1 | B’ |
1 | 1 | 0 | B |
1 | 1 | 1 | B |
The simplification of the truth table by using the “don’t care”:
I0 | I1 | I2 | I3 | |
B’ | 0 | 1 | 4 | 5 |
B | 2 | 3 | 6 | 7 [Don’t care] |
B | 1 | B | If “7” is considered then 1 Or B’ |
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