GATE CS 2020 Q28 — Boolean Algebra

The given logic circuit consists of:

• A NOT gate with input $b$, producing $\bar{b}$.
• An AND gate with inputs $\bar{b}$ and $c$, producing the term $\bar{b}c$.
• An OR gate with inputs $a$ and $\bar{b}c$, producing the final output:

To find the minterm list, we expand each term into its canonical sum-of-products (SOP) form:

• For the term $a$ (where $a = 1$):
  The variables $b$ and $c$ can take any binary value, corresponding to the binary combinations $100_2, 101_2, 110_2, 111_2$.
  This gives the minterms: $\{4, 5, 6, 7\}$.
• For the term $\bar{b}c$ (where $b = 0$ and $c = 1$):
  The variable $a$ can be either $0$ or $1$, corresponding to $001_2$ and $101_2$.
  This gives the minterms: $\{1, 5\}$.

Taking the union of these minterms, we get:

Thus, the correct option is B.