Project ForgeDigital Logic
Combinational & Sequential Circuits
GATE 2010
Hard
The Boolean expression for the output f of a 4-to-1 multiplexer with inputs I0=R, I1=R̄, I2=R̄, I3=R (select lines S1=P, S0=Q) is
- Acomplement of (P⊕Q⊕R)
- P⊕Q⊕R
- CP+Q+R
- Dcomplement of (P+Q+R)
Explanation
f=R when (P,Q)∈{(0,0),(1,1)} (P=Q), and f=R̄ when (P,Q)∈{(0,1),(1,0)} (P≠Q). Letting X=P⊕Q (true exactly when P≠Q), f = X̄·R + X·R̄ = X⊕R = (P⊕Q)⊕R = P⊕Q⊕R.
Source: GATE CS 2010 (2010)
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