Consider the circuit below and find the output function f(x, y, z). Assume a…
2012
Consider the circuit below and find the output function f(x, y, z). Assume a standard 2:1 MUX convention: select 0 chooses the input labelled 0 and select 1 chooses the input labelled 1.
- A.
xz′ + xy
- B.
xz′ + xy + y′z′
- C.
xz + xy + y′z′
- D.
xz + xy′ + y′z
Attempted by 62 students.
Show answer & explanation
Correct answer: A
Answer: xz′ + xy
Step 1: First MUX
The first MUX has input 0 = x, input 1 = y, and select = z. So its output is:
M = z′x + zyStep 2: Second MUX
The second MUX has input 0 = M, input 1 = x, and select = y. Therefore:
f = y′M + yxStep 3: Substitute and simplify
f = y′(z′x + zy) + yx
= xy′z′ + y′zy + xy
= xy′z′ + xy
= x(y′z′ + y)
= x(z′ + y)
= xz′ + xyTherefore, the output function is xz′ + xy.
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