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Homework Statement
Design a multiplexer circuit given the data such that:
When ##C = 0##, the output ##X = A##.
When ##C = 1##, the output ##X = B##.
The truth table is displayed below:
Homework Equations
The Attempt at a Solution
I wanted to make sure I understood this and I wasn't overlooking anything.
Looking at the ##A##, ##C## and ##P## columns, I deduced I needed a term of the form ##A \cdot \bar C##.
Looking at the ##B##, ##C## and ##Q## columns, I deduced I needed a term of the form ##B \cdot C##.
Looking at the ##P##, ##Q## and ##X## columns, I see I need a gate that satisfies ##\bar P \cdot Q + P \cdot \bar Q + P \cdot Q##.
That last expression can be simplified to:
##\bar P \cdot Q + P \cdot \bar Q + P \cdot Q = \bar P \cdot Q + P(\bar Q + Q) = \bar P \cdot Q + P = Q + P##
So from what I can gather, ##Q + P = B \cdot C + A \cdot \bar C##.
Hence ##X = Q + P = B \cdot C + A \cdot \bar C##.
Thank you.