How can I draw the diagram using few decoders for this truth table?

Question

For the truth table above, abc is the input and xyz is the output.

I do know how to draw the diagram using a decoder in case of when I have only one output. How can I draw the diagram using a decoder when I have 3 outputs for this case?

This is what I am guessing

After I apply the advice, here is what I have

Start by showing what you tried to solve it. It helps us to see where you're running into trouble, or just to feel like we're not doing your homework for you. — Drew Macrae, May 15 '19 at 15:59
@andrewMacrae I appreciate your help! I tried based on what you said! — Sangmin Choi, May 15 '19 at 16:49
@stainlesssteelrat Got it. I could see z = c. What does it mean by the way? Do I still need to keep the or gate for z like above? — Sangmin Choi, May 15 '19 at 17:22
It just means there is no difference between z OR c, so no logic is needed. c on one end of a line, z on the other. Your instructor wants you to think about what logic design actually means. — StainlessSteelRat, May 15 '19 at 20:26
@StainlessSteelRat okay. But, I am confused with "no logic is needed". Do you mean that I do not need to put any logic gate for z? So just do nothing for the z?.. — Sangmin Choi, May 15 '19 at 21:17
A line with c on left and z on right. As in, no OR, no Mux, just a line. — StainlessSteelRat, May 15 '19 at 22:07

score 0 · Accepted Answer · answered May 15 '19 at 16:22

it looks like you nearly have it.

X is high if the input decodes to the '100 value, Y is high if it decodes to '010, '011, '101 or '110 and Z is high if it decodes to '001 '011 '101 or '111.

There is one error in your drawing: X, Y and Z are already your outputs. You don't need to "or" them together at the end.

Then take a look at the drawing and see if you can understand how the ABC decoders are redundant and how you can reuse the outputs from just one decoder to compute X, Y and Z so you only need one decoder.

How can I draw the diagram using few decoders for this truth table?

1 Answers1