GATE CS 2026 Set 2 Q30 — Minimization (K-Maps etc.)

To find the minimal sum of products (SOP) form for the Boolean function $F(A, B, C, D) = \Sigma m(0,1,2,3,8,9,10,11)$, we can analyze the binary representations of the given minterms:

• $m_0, m_1, m_2, m_3 \implies 0000, 0001, 0010, 0011$ (which simplifies to $A'B'$)
• $m_8, m_9, m_{10}, m_{11} \implies 1000, 1001, 1010, 1011$ (which simplifies to $AB'$)

Combining these two groups of 4 minterms, we get a single group of 8 minterms (an octet):

In a 4-variable K-map, these 8 cells form a single octet where the variable $B$ is constantly $0$ while $A$, $C$, and $D$ vary across all possible combinations. Thus, the minimal SOP expression is $B'$.