Design the logic circuit

• Engineering
• STEMucator

Homework Helper

Homework Statement

Draw the simplest logic gate or circuit for the description below. The inputs are ##a, b, c## and the output is ##z##.

##z = 0## only if ##abc = 010## or ##abc = 110##

The Attempt at a Solution

So i drew up a quick table, AND and OR'ed the required terms together and came up with this:

Is this okay? The input ##a## seems to have disappeared, which makes no sense to me. Unless its some sort of trick question where I only need 2 inputs since the output doesn't rely on ##a## at all.

Also, have you tried plugging the two values back into your answer...?

I'm trying to do this without a K-Map.

Plugging the values of ##b## and ##c## into my answer does provide the correct output, but I am unsure about the input ##a##.

I don't believe the answer is correct, and I am unsure how to algebraically simplify this if my above attempt is incorrect.

My apolgies! I missed in your OP that z=0 for those two terms. Your answer does look correct. Sorry for any confusion I caused...

My apolgies! I missed in your OP that z=0 for those two terms. Your answer does look correct. Sorry for any confusion I caused...

Thank you for the clear up. I was just slightly confused about the inputs, but the logic worked out that way I guess.

z= 0 only if abc=010abc = 010 or abc=110
You did well. An alternative is to write ##\bar z\ =\ \bar a b \bar c\ +\ ab\bar c##

Then simplify this as you did with your expression earlier, to get z = ...

The answers will be the same. :)