Answer to Question #240017 in Electrical Engineering for Ramakrishna Reddy

Question

A Boolean function fk of two variables A and B is defined as follows:
fk (0, 0) = fk (0, 1) = fk (1, 1) = 1; fk (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.

Answer 1

Provided:

1.     The definitions of the Boolean Functions are as follows:

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

2.     Given that A and B variables for the above lack complements

3.     We need to obtain the minimum cost for realizing 2 input nor gates and 2 input or gates are required to realize:

We understand that the inclusive NOR (Not-OR) gate has an output that 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, we will have

For the OR gate, plus NOT gate we will have :

The truth table cable is represented as follows: