Answer to Question #241759 in Electrical Engineering for Mani

Question #241759
A Boolean function f of two variables A and B is defined as follows.

fi (0,0) = f (0, 1) = f (1.1) = 1; fi (1,0) = 0

Assuming complements of A and B are not available, what will be the minimum cost solution for realizing using only 2-input NOR gates and 2-input OR gates (each having unit cost)? Explain with nessessary digram and expression.
Expert's answer

Notably, the inclusive NOR (Not-OR) gate gives an output which is normally at logic level “1” and only goes “LOW” to logic level “0” when ANY of its inputs are at logic level “1”. The Logic NOR Gate is the reverse or “Complementary” form of the inclusive OR gate.

Also we know that If both A and B are NOT true, then Q is true” from a general perspective which in this case is defined as:

f k (0, 0) = fk (0, 1) = fk (1, 1) = 1; fk (1, 0) = 0

For the NOR gate, 

Thus we obtain have

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