Consider the following 4-variable Boolean function $$F(A, B, C, D) = \Sigma m(0, 1, 2, 3, 8, 9, 10, 11)$$ Consider $A$ as MSB, $D$ as LSB. Which one of the following options represents the minimal sum of products form for the above function? Note: $+$ is OR operation, $.$ is AND operation, $'$ is NOT operation

The Boolean function is given by the minterms:

Expressing the minterms in terms of their binary representations $(A B C D)$:

• $m(0, 1, 2, 3)$ correspond to $A = 0, B = 0$ with all combinations of $C$ and $D$, which simplifies to $A^{\prime}B^{\prime}$.

• $m(8, 9, 10, 11)$ correspond to $A = 1, B = 0$ with all combinations of $C$ and $D$, which simplifies to $AB^{\prime}$.

Combining these two sets of minterms in a 4-variable Karnaugh Map (K-map):

• The octet formed by combining the first row ($AB = 00$) and the fourth row ($AB = 10$) covers all 8 minterms.

• In these two rows, variable $B$ remains constant at $0$ (i.e., $B^{\prime}$), while variables $A$, $C$, and $D$ change and are eliminated.

Thus, the minimal sum of products form is $B^{\prime}$, corresponding to option (B).