Consider a multiplexer with X and Y as data inputs and Z as control input. Z =…
2004
Consider a multiplexer with X and Y as data inputs and Z as control input. Z = 0 selects input X, and Z = 1 selects input Y. What are the connections required to realize the 2-variable Boolean function f = T + R, without using any additional hardware ?
- A.
R to X, 1 to Y, T to Z
- B.
T to X, R to Y, T to Z
- C.
T to X, R to Y, 0 to Z
- D.
R to X, 0 to Y, T to Z
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Correct answer: A
Solution: Realize f = T + R using the multiplexer connections below.
Multiplexer operation: when the select input Z = 0, output = X; when Z = 1, output = Y.
Choose connections: X = R, Y = 1 (logic high), Z = T.
Derive the output:
If T = 0 (Z = 0) output = X = R → contribution R·¬T.
If T = 1 (Z = 1) output = Y = 1 → contribution 1·T = T.
Combine contributions: f = R·¬T + T. Using Boolean algebra, R·¬T + T = T + R, so the required function is realized without extra hardware.
Note: Other connection choices fail because they produce different expressions (for example, mapping X=T, Y=R, Z=T gives R·T; tying Z=0 yields T; mapping Y=0 yields R·¬T).