The min terms for the following 'fmin' will be:

47. The min terms for the following 'f_min' will be:

f_min = A'C' + A'D + A'B + BD

• A. f = Σ_m(0, 1, 5, 6, 9, 13, 15)
• B. f = Σ_m(2, 8, 9, 10, 12, 14)
• C. f = Σ_m(0, 1, 3, 4, 5, 6, 7, 13, 15)
• D. f = Σ_m(1, 5, 7, 9, 10, 12, 14, 15)

Answer: Option C

Solution

Finding Minterms for the Boolean Expression

Given Boolean expression:

F_min = A'C' + A'D + A'B + BD

We determine all combinations of A, B, C, and D for which the function is equal to 1.

1. A'C'

Here A = 0 and C = 0, while B and D can be anything.

• 0000 = m₀
• 0001 = m₁
• 0100 = m₄
• 0101 = m₅

2. A'D

Here A = 0 and D = 1, while B and C vary.

• 0001 = m₁
• 0011 = m₃
• 0101 = m₅
• 0111 = m₇

3. A'B

Here A = 0 and B = 1, while C and D vary.

• 0100 = m₄
• 0101 = m₅
• 0110 = m₆
• 0111 = m₇

4. BD

Here B = 1 and D = 1, while A and C vary.

• 0101 = m₅
• 0111 = m₇
• 1101 = m₁₃
• 1111 = m₁₅

Final Minterm Form:

F(A,B,C,D) = Σm(0,1,3,4,5,6,7,13,15)

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