Question

Find an expression to represent the final column E of the truth table. Simplify if possible.

A	B	C	E
1	1	1	1
1	1	0	0
1	0	1	0
1	0	0	1
0	1	1	1
0	1	0	0
0	0	1	0
0	0	0	0

Answer 1

As we inspect the E-column of the truth table, we see that E assumes the truth value 1 for combination numbers 1, 4, 5. Considering only these combinations and ignoring the others, we write the minterms for these combinations and taking sum of these minterms we get the full disjunctive canonical form of E as :

E = ABC+AB'C'+A'BC

i.e., E = ABC+A'BC+AB'C'

i.e., E = (A+A').BC+AB'C'

i.e., E = I.BC+AB'C'

i.e., E = BC+AB'C'

This is the representation of the final column E.