Question

Simply the following Boolean function F, together with the don't-care conditions d, and then express the corresponding simplified function in sum of minterms: (a) F(x,y,z)=Σ(1,4,6)d(x,y,z)=Σ(0,2,7) (b) F(A,B,C,D)=Σ(1,5,6,7,13) d(A,B,C,D )=Σ(8,4)

Answer 1

To simplify the given Boolean functions, we combine the minterms based on their common terms and express the simplified function in sum of minterms.

Step-by-step explanation:

To simplify the given Boolean function F, we need to combine the minterms based on their common terms. Let's start with part (a):

F(x,y,z)=Σ(1,4,6)

d(x,y,z)=Σ(0,2,7)

By combining the minterms, we get:

F(x,y,z) = x'yz + xyz' + xy'z

Next, let's simplify part (b):

F(A,B,C,D)=Σ(1,5,6,7,13)

d(A,B,C,D)=Σ(8,4)

By combining the minterms, we get:

F(A,B,C,D) = A'B'CD + A'B'CD' + AB'CD + ABCD' + ABC'D'