Question

construct a truth table for the boolean expression x = ab + bc

Explanation:

Step1: List all possible input combinations

There are 3 variables A, B, and C. Each variable can have 2 values (0 or 1). So, there are \(2^3 = 8\) combinations: (0,0,0), (0,0,1), (0,1,0), (0,1,1), (1,0,0), (1,0,1), (1,1,0), (1,1,1).

Step2: Calculate AB for each combination

When A = 0 and B = 0, AB = 0; when A = 0 and B = 1, AB = 0; when A = 1 and B = 0, AB = 0; when A = 1 and B = 1, AB = 1.

Step3: Calculate BC for each combination

When B = 0 and C = 0, BC = 0; when B = 0 and C = 1, BC = 0; when B = 1 and C = 0, BC = 0; when B = 1 and C = 1, BC = 1.

Step4: Calculate AB + BC for each combination

Use the OR - operation rules (0+0 = 0, 0 + 1=1, 1+0 = 1, 1 + 1=1).

A	B	C	AB	BC	AB + BC
0	0	1	0	0	0
0	1	0	0	0	0
0	1	1	0	1	1
1	0	0	0	0	0
1	0	1	0	0	0
1	1	0	1	0	1
1	1	1	1	1	1

Answer:

The truth - table is shown above.