How do you draw these logic circuits?

Question

I need to make a logic circuit ffrom the truth table below for output X

1. A circuit using AND gate, or gates and NOT gates

2. A circuit using NAND gates and NOT gates

3. A circuit using other gates that make it simpler.

Here is the truth table:

(sorry for the allignment)

The inputs are D C B A and the out put is X

D C B A X

0 0 0 0 0

0 0 0 1 0

0 0 1 0 0

0 0 1 1 0

0 1 0 0 1

0 1 0 1 1

0 1 1 0 1

0 1 1 1 1

1 0 0 0 1

1 0 0 1 1

1 0 1 0 1

1 0 1 1 1

1 1 0 0 0

1 1 0 1 0

1 1 1 0 0

1 1 1 1 0

I really don't know how to go about this. I have read through web links etc and attempted this myself but with no luck.

I am desperate for help, thanks to all that can.

Answer 1

Concentrate on the middle section.

8 4 2 1

0 1 0 0 1

0 1 0 1 1

0 1 1 0 1

0 1 1 1 1

1 0 0 0 1

1 0 0 1 1

1 0 1 0 1

1 0 1 1 1

the rest don't count because they all lead to a false output.

Notice the patterns. The output is true when B8 and B4 are 01 or 10

(B4 and not B8) or (B8 and not B4) will do it.

I thought it would be complicated, but it's actually quite simple. 4 gates.

Two inverters to invert B4 and B8, then two AND gates and one OR gate.

.

Answer 2

In general, you need C high, or D high, but not both.  Answering # 3 first, X = C xor D.

1.  X = (C AND NOT D) OR (NOT C AND D).

I'll let you work out 2 from 1, with the hint that you'll need DeMorgan's theorm.