What is the minimum number of 2-input NOR gates required to implement a 4-variable function expressed in sum of-min-terms form as f = ∑(0, 2, 5, 7, 8, 10, 13, 15)?

Assume that all the inputs and their complements are available.

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Answer (Detailed Solution Below) 3

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Let us assume that A, B, C, and D are the 4 variables.

K- map for given function:

f(A, B, C, D) = BD + B̅ D̅

Implementing the above function by using XOR gates with complements of variables:

f(A, B, C, D) = BD + B̅ D̅

Therefore, the minimum number of 2-input NOR gates needed to implement the function is 3.

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