NIMCET 2009 — Computer PYQ

To find the simplified switching expression, we map the given minterms $\{1,4,5,9,11,12\}$ onto a 4-variable Karnaugh Map (K-Map).

K-Map Representation:

Grouping the Minterms:

1. Group 1 (m4, m5): This is a pair in the second row. $A=0,B=1$ are constant, and $C=0$ is constant. The expression is $\overline{A}B\overline{C}$. Wait, let's look at the options provided. The options suggest a different grouping or a Sum of Products (SOP) that isn't fully minimized or uses different overlaps.

2. Checking Option (a): Let's verify if the terms in option (a) cover the minterms.

   • $B\overline{C}\overline{D}$ covers $\{4,12\}$.

   • $\overline{A}\overline{C}D$ covers $\{1,5\}$.

   • $A\overline{B}D$ covers $\{9,11\}$.

   • Combined: $\{1,4,5,9,11,12\}$. This perfectly matches the given function.

Conclusion:

Option (a) correctly represents the switching expression as it covers all the specified minterms exactly.