Question

3u. expand the function, f(a3, a2, a1, a0) = a3a2 (a1’ a0).a3’ to its canonical or standard product-of-sum (pos) and sum-of-product (sop) forms:

Answer 1

Answer: To expand f(a3, a2, a1, a0) = a3a2 (a1’ a0).a3’ to its canonical or standard product-of-sum (POS) and sum-of-product (SOP) forms:

First, we will write out the function in SOP form:
f(a3, a2, a1, a0) = a3a2(a1’ a0).a3’
= (a3 + a2 + a1’ + a0)(a3’)
= a3’a3 + a2a3’ + a1’a3’ + a0a3’

Next, we will write out the function in POS form:
f(a3, a2, a1, a0) = a3a2(a1’ a0).a3’
= (a3 + a2 + a1’ + a0)(a3’)
= (a3 + a3’)(a2 + a3’)(a1’ + a3’)(a0 + a3’)
= (a3 + a2 + a1’ + a0)(a3 + a2 + a1’ + a0’) (a3 + a2 + a1 + a0’) (a3 + a2’ + a1’ + a0’)

Therefore, the POS form of the function is (a3 + a2 + a1’ + a0)(a3 + a2 + a1’ + a0’) (a3 + a2 + a1 + a0’) (a3 + a2’ + a1’ + a0’), and the SOP form of the function is a3’a3 + a2a3’ + a1’a3’ + a0a3’.