Given the Boolean expression F = x’y + xyz’:?

Question

Given the Boolean expression F = x’y + xyz’:
Derive an algebraic expression for the complement F’ and then draw its Logic diagram.

Answer 1

I assume x' means not x
(xy)' = x' + y'
(x+y)' = x' y'

F = x'y+xyz'
F' =( x'y)' (xyz')' = ( x''+y')(x'+y'+z'') = (x+y')(x'+y'+z)
= xy' +xz +y'x'+y' +y'z
= x(y'+z)+y'

Answer 2

i'm no longer certain what you mean via algebraic expression, notwithstanding the reality table (good judgment diagram?) could be: x y z F 0 0 0 0 0 0 a million 0 0 a million 0 a million 0 a million a million a million a million 0 0 0 a million 0 a million 0 a million a million 0 a million a million a million a million 0

Answer 3

x’y + xyz’ =
y(x' + xz') =
y(x' + z')

(y(x' + z'))' =
y' + (x' + z')' =
y' + xz

Truth Table:
.x y z F'
0 0 0 1
0 0 1 1
0 1 0 0
0 1 1 0
1 0 0 1
1 0 1 1
1 1 0 0
1 1 1 1
edit:
Logic Diagram:
y' + xz
. . y y'
x 0 1 z'
x 1 1 z
x' 0 1 z
x' 0 1 z'

Answer 4

F' = (x+y')(x'+y'+z)

It's difficult to draw the diagram in this text box.


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