The switching expression corresponding to f(A, B, C, D) = Σ (1, 4, 5, 9, 11,…

Final minimal switching expression: BC'D' + A'C'D + AB'D

• Step 1: List the minterms given by the function:

  Minterms: 1 (0001), 4 (0100), 5 (0101), 9 (1001), 11 (1011), 12 (1100).

• Step 2: Form pairs of minterms that differ by only one variable to get prime implicants:

  • Pair 4 (0100) and 12 (1100) → common B=1, C=0, D=0 ⇒ BC'D'.

  • Pair 1 (0001) and 5 (0101) → common A=0, C=0, D=1 ⇒ A'C'D.

  • Pair 9 (1001) and 11 (1011) → common A=1, B=0, D=1 ⇒ AB'D.

• Step 3: Verify coverage and minimality:

  The three implicants BC'D', A'C'D, and AB'D together cover all given minterms (1, 4, 5, 9, 11, 12). No implicant can be dropped without leaving some minterm uncovered, so the expression is minimal.