How do I create a circuit based on a Boolean function using only a multiplexer?

Question

I need to create a circuit based on the Boolean function: Y = AB’ + B’C’ + A’BC using only an 8 to 1 multiplexer. Then recreate the circuit using only a 4 to 1 multiplexer and NOT gates.

I figured the truth table to be:

A   B    C    |    Y
0   0    0    |    1
0   0    1    |    0
0   1    0    |    0
0   1    1    |    1
1   0    0    |    1
1   0    1    |    1
1   1    0    |    0
1   1    1    |    0

But I don't understand how to make the circuit using only a 8 to 1 multiplexer.

This question appears to be off-topic because hardware design questions belong on [electronics.se] — , Oct 25 '14 at 17:53

score 0 · Answer 1 · answered Jun 08 '16 at 14:47

Well, 1- Take an 8 to 1 multiplexer 2- Connect A, B y C to the three input 3- connect Y0, Y3, Y4 and Y5 to Vcc, and the rest to ground.

This logical function is made with just one 3x1 multiplexer and no other component.

To make it with 4x1, yo need to connect, for example A and B to the two control inputs, and the 4 input Y0, Y1, Y2, Y3 to the Vcc, ground, C or not(C) as needed, but yo need at least one not gate.

It seem as there is not a solution without a not gate, because por A=B=C=0->Y=1, and A=B=C=1->Y=0

How do I create a circuit based on a Boolean function using only a multiplexer?

1 Answers1