Help With This Truth Table, Logic Gates and Karnaugh Map?

Question

INPUTS OUTPUTS

D C B A X Y

0 0 0 0 0 1

0 0 0 1 0 1

0 0 1 0 0 0

0 0 1 1 0 0

0 1 0 0 1 1

0 1 0 1 1 1

0 1 1 0 1 0

0 1 1 1 1 0

1 0 0 0 1 0

1 0 0 1 1 0

1 0 1 0 1 0

1 0 1 1 1 0

1 1 0 0 0 X

1 1 0 1 0 X

1 1 1 0 0 X

1 1 1 1 0 X

In the Truth Table the inputs are :a, b, c, d and the outputs are X, Y

Q1. Use a karnaugh map to come up with the minimum sum of products form when

X and when Y.

Q2. Draw the circuit using AND gate, OR gates and NOT gates.

Q3. Draw the circuit using NAND gates and NOT gates.

Q4. Come up with a simpler way to draw the circuit using other types of gates

I am basically finding it hard to understand the truth table and go about answering the questions for it.

Apologies for not lining the columns up properly

Help Is Desperately Needed Thanks To Everyone That Can Contribute

Answer 1

What I can see is that A does not contribute to the answer. It is also apparent that Y is B XOR C and X is C XOR D. This would give you the simplified answer. I'm also not sure why there are four Xs in the corner, but maybe you do.

So X = C XOR D, or ((C OR D) AND (NOT (C AND D))), or (NOT (((NOT C) NAND (NOT D)) NAND (C NAND D)))

and Y = B XOR C, or ((B OR C) AND (NOT (B AND C))), or (NOT (((NOT B) NAND (NOT C)) NAND (B NAND C)))

That should answer 2-4, but I'm not sure how to use a karnaugh map.