Consider the two cascaded 2-to-1 multiplexers as shown in the figure The…
2016
Consider the two cascaded 2-to-1 multiplexers as shown in the figure
The minimal sum of products form of the output \(X\) is
- A.
\(\overline{P} \ \overline {Q}+PQR\) - B.
\(\overline{P} \ {Q}+QR\) - C.
\(PQ +\overline{P} \ \overline{Q}R\) - D.
\(\overline{Q} \ \overline{R} + PQR\)
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Correct answer: D
Key insight: analyze what each multiplexer outputs depending on its select line.
Left MUX (select = P): selects between 0 (when P = 0) and R (when P = 1). So its output is P·R.
Right MUX (select = Q): when Q = 0 it outputs ¬R; when Q = 1 it outputs the left MUX output (PR).
Combine the two cases: X = ¬Q·¬R + Q·(P·R) = ¬Q·¬R + P·Q·R. This is already the minimal sum-of-products form.
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