NIMCET 2023 — Computer PYQ
NIMCET | Computer | 2023The reduced form of the Boolean Function F = xyz + xyz' + x'yz + xy'z is
Choose the correct answer:
- A.
xy+yz
- B.
x+yz+xz
- C.
x+ y +z
- D.
xy+yz +xz
(Correct Answer)
xy+yz +xz
Explanation
F=xyz+xyz′+x′yz+xy′z.
xy+yz
We can factor out y from the first two terms: y(xz+z′). The
expression xy+yz is not equivalent to F.
x+yz+xz
We can factor out z from the first and last terms: xz(y+x′+1).
The expression x+yz+xz is not equivalent to F.
x+y+z
This expression is not equivalent to F as it does not contain the
term xy′z.
xy+yz+xz
We can see that this expression matches the given Boolean
function F. It is the reduced form of F. Therefore, the correct reduced form of
F=xyz+xyz′+x′yz+xy′zisxy+yz+xz.
Explanation
F=xyz+xyz′+x′yz+xy′z.
xy+yz
We can factor out y from the first two terms: y(xz+z′). The
expression xy+yz is not equivalent to F.
x+yz+xz
We can factor out z from the first and last terms: xz(y+x′+1).
The expression x+yz+xz is not equivalent to F.
x+y+z
This expression is not equivalent to F as it does not contain the
term xy′z.
xy+yz+xz
We can see that this expression matches the given Boolean
function F. It is the reduced form of F. Therefore, the correct reduced form of
F=xyz+xyz′+x′yz+xy′zisxy+yz+xz.