A Logic Problem

A Logic Problem (5.1)

Dr. Abner Mallity has been working with a counter circuit. He has a counter that requires the following:

To count up, hold pin D high (5v), and put the pulse into pin U.
To count down, hold pin U high (5v), and put the pulse into pin D.

What Mallity wants is a circuit that will do the following.

To count up, hold pin X high (5v) and put the pulse to be counted into pin Y.
To count down, hold pin X low (0v) and put the pulse to be counted into pin Y.
i.e. he wants a box that does this:

Your Job:

Your job is to design the "stuff" inside the box.

The first thing to do is to get a truth table. Here is the first shot at a truth table. The one thing we know, is that we want D high when we want to count up (X = 1) and we want D low when we want to count down (X = 0). We can fill in that part of the table.

X	Y	U	D
0	0	1
0	1	1
1	0		1
1	1		1

Next, we want to pulse to go into D when we want to count down, and into U when we want to count up. That simply means that D = 0 when the pulse is 0 and D = 1 when the pulse is 1.

X	Y	U	D
0	0	1	0
0	1	1	1
1	0	0	1
1	1	1	1

That gives us the complete truth table, and we can write the function from the truth table.

D = X + Y (Pretty straight-forward, and it gives us a clue that the other function is something like that as well.
U = (~X) + Y

The implementation is pretty straight-forward, and we don't show it here.