Consider the Boolean expression A(x, y, z) = x (y′ + z′).
Which of the following is the complete sum-of-products form of the given Boolean expression?
Solution
Given,
A = x (y′ + z′)
= xy′ + xz′
To express as a complete sum-of-products, expand using all variable combinations:
= xy′(z + z′) + xz′(y + y′)
= xy′z + xy′z′ + xyz′ + xy′z′
After simplification, duplicate terms are removed:
A = xyz′ + xy′z + xy′z′