Question

Write POS Boolean expressions for F (a, b) = ab'+a'b. Show through Boolean algebra reduction that the SOP & POS expressions are indeed equivalent to one another.

Answer 1

Given:

F(a,b) = ab′ + a′b

This is the SOP form.

To write the POS form, use the rows where F = 0.

For ab′ + a′b, the output is 0 when:

(a, b) = (0, 0), (1, 1)

So the POS form is:

F = (a + b)(a′ + b′)

Now prove both are equivalent.

(a + b)(a′ + b′) ​= aa′ + ab′ + ba′ + bb′

= 0 + ab′ + a′b + 0

= ab′ + a′b​

Therefore,

(a + b)(a′ + b′) = ab′ + a′b