Boolean algebra minimization

Question

F = ABC + AC + C'D'

is there a way to minimise this function even further because i want to make the circuit diagram with only 2 input nand gates

any suggestions ? thanks

Answer 1

First, simplify:

F = ABC + AC + C'D'
F = AC(B + 1) + C'D'
F = AC + C'D'

Now, put in terms of ANDs and NOTs only:

F = (AC + C'D')''        [double negation]
F = ( (AC)'(C'D')' )'    [DeMorgan's]

Then noting that:

• NOT can be implemented via 2-input NAND by tying its inputs together.
• AND can be implemented via 2-input NAND by combining NAND and NOT.

You should be able to implement F in this form directly using only 2-input NANDs.

Answer 2

This is the solution for the minimalization using a Karnaugh Table.