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I have a problem with some homework, for my Advanced Digital Design course, in which I have to create the truth table and find the Boolean expression for a provided circuit (image is linked below). I was able to create the truth table and I think find the Boolean Expression for the problem using the truth table that I created, but I don't think that this is the way that we are supposed to find the Boolean Expression. I was hoping that someone could share some insight on how to find the Boolean Expression without using the truth table.

I would normally not have such an issue with this, but since there are 5 variables, and NAND gates, I am quite confused on how to simplify once I find it.

I think that the outcome is something like: [(a(bcd)'e)']' when you look at the circuit, and not the table, but I am not entirely sure. I am also not sure on how to simplify this into a Boolean expression if this is right.

Using the truth table to find the minterms I get y= m17+m19+m21+m22+m23+m25+m29 (which I am also not sure if it is right). And if I use a K-Chart to solve this, I end up with y = ab'e + a'ce + ab'cd, which seems like a legitimate simplified Boolean expression, but I have no clue if that is right.

Since this question is worth 20 of the total 100 points, I could really use some help understanding how this works.

Here is the image we were provided: Circuit: only circuit (a), not (b)

enter image description here

Thank you!

Alain Merigot
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Cait_L
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1 Answers1

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I think that the outcome is something like: [(a(bcd)'e)']'

Your first guess is correct.

You just have to remark that whatever''=whatever

f=[(a(bcd)'e)']' = a(bcd)'e

Using de Morgan (bcd)' = b'+c'+d'

Hence f=a(bcd)'e = ae(b'+c'+d') =ab'e + ac'e + ad'e

which is minimal.

Alain Merigot
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