Question

1. Simplify the following Boolean function to sum-of-product by first finding the essential prime implicant              F(A, B, C, D) = ∑( 0, 1, 3, 4, 5, 7, 9, 11, 13)

2. Implement the simplified Boolean function in 1. Using NOR gates only

Answer 1

Solution 1:-

There are 4 prime implicants and 4 essential prime implicants for the given minterms using K-map Boolean expression has been derived and the essential prime implicants are also found.

Essential prime implicants table:-

^ ^ v ^ ^ ^ 80 AD ✓ ^ ^ ^ v ^ C D lallo ^ لا 0 13 17 th h نر -

K-map and Boolean expression:-

FRA,B,C ,D) ē Ã ī D CD c) Ã Ā B Quad Co, 1,4,5) Quad (1,5,9, 13:00 Quad (1,3,5,7) :ÃO Quad (1,3,9,11): 50 Ã łt EDTĀD+ BD AB AB F

Solution 2:-

The function has been constructed using only NOR gates.

A B ED BD . AD Ã