Question

Simplify the following Boolean function F, together with the don't-care conditions d, and then express the simplified function in sum-of-minterms form:

F (x, y, z) = Σ(0, 1, 4, 5, 6)
d(x, y, z) = Σ(2, 3, 7)

Answer 1

To simplify the Boolean function F(x, y, z) = Σ(0, 1, 4, 5, 6) with the don't-care conditions Σ(2, 3, 7), combine the minterms and the don't-care terms. Group the minterms with their common variables and write the simplified function in sum-of-minterms form.

Step-by-step explanation:

To simplify the Boolean function F, we will first write down the minterms associated with the given function and the don't-care conditions.
F(x, y, z) = Σ(0, 1, 4, 5, 6) d(x, y, z) = Σ(2, 3, 7)

Next, we will combine the minterms and the don't-care terms.
F = Σ(0, 1, 2, 3, 4, 5, 6, 7)

We will then group the minterms with their common variables and write the simplified function in sum-of-minterms form.
F = x'y'z' + xy' + xz' + yz'