ABC X Y

000 0 0

001 1 1

010 0 0

011 0 0

100 0 1

101 1 1

110 1 0

111 1 0

a) Find the Boolean expression for the truth table shown and then implement each output seperately using the minimum number of two input Nand gates.

b) Show how you could combine the two circuits to make a three input two output circuit with two input Nand gates using less gates than the original two circuits.

Ok... The main bit im stuck on is creating a Boolean expression for the full table.

For X output - X = AB + B'C (Simplified)

For Y output - Y = AB' + B'C (Simplified)

To simplify these I have used the Idempotent law as I need to build these using only two input Nand gates.

For the full table I think the simplified expression would be:

B'C + AC' + AB

Could anyone confirm these answers for me? Also do you think for b) it just means design a circuit for the full expression?

Cheers,

Simon.