Question

Show the minimized POS form of the Boolean function F(A,B,C) = ∑m(0,1,2,4,5) and show its realization using only NOR gates.

Answer 1

To minimize the Boolean function F(A,B,C) = ∑m(0,1,2,4,5) into a POS (Product of Sums) form, we need to find the groups of minterms that have the same output value in the truth table. The minimized POS form of the Boolean function is F(A,B,C) = A'B' + A'C' + B'C'. To realize this function using only NOR gates, we can implement each term in the POS expression using a NOR gate.

Step-by-step explanation:

To minimize the Boolean function F(A,B,C) = ∑m(0,1,2,4,5) into a POS (Product of Sums) form, we need to find the groups of minterms that have the same output value in the truth table. Looking at the given minterms:

0: A'B'C'
1: A'B'C
2: A'BC'
4: AB'C
5: ABC

If we group the minterms that have an output value of 1, we get:

(0,2,4): A'B' + A'C' + B'C'

The minimized POS form of the Boolean function is F(A,B,C) = A'B' + A'C' + B'C'. To realize this function using only NOR gates, we can implement each term in the POS expression using a NOR gate.