Question

Simplify the following Boolean expression using
K-map :
F(a, b, c) = Σ (1, 2, 4, 5, 6, 7)
and realize the same using NOR gates.

Answer 1

Solution of K Map

There are the following steps to find the solution or K-map:

Step 1:

Firstly, we define the given expression in its canonical form.

Step 2:

Next, we create the K-map by entering 1 to each product-term into the K-map cell and fill the remaining cells with zeros.

Step 3:

Next, we form the groups by considering each one in the K-map.

Simplification of boolean expressions using KMap

Notice that each group should have the largest number of 'ones'. A group cannot contain an empty cell or cell that contains 0.

Simplification of boolean expressions using Map

In a group, there is a total of 2n number of ones. Here, n=0, 1, 2, n.