Question

For the Boolean function F = x + yz’+ x’z

1. Show the truth table.
2. Simplify F by using k-map as SoP form.

Answer 1

The truth table for the given boolean function F = x + yz' + x'z

If x is 0 then x' is 1 and same for y and z too

to calculate yz' is using AND gate (performs multiplication) and same for x'z

for calculation of x+yz' we use OR gate (peforms Addition) and for x+yz'+x'z

x	y	z	x'	y'	z'	yz'	x'z	x+yz'	x+yz'+x'z
0	0	0	1	1	1	0	0	0	0
0	0	1	1	1	0	0	1	0	1
0	1	0	1	0	1	1	0	1	1
0	1	1	1	0	0	0	1	0	1
1	0	0	0	1	1	0	0	1	1
1	0	1	0	1	0	0	0	1	1
1	1	0	0	0	1	1	0	1	1
1	1	1	0	0	0	0	0	1	1

SOP (Sum of Products) is used for min-terms and we can cleary see that equation is given in the SOP form.

By min-terms I mean if there is x then it will taken as 1 and if it is x' it will be taken as 0 in the K-map

We will use the K-map for simplification of the boolean function:

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

Simplified function is F = x'y'

We will make pair and check and form the equation. Since x is not changing then we will consider x and also y is not changing which we can clearly in the k-map and both of them are 0 so we will take x' and y'