# Building a logic circuit from a truth table

• Engineering
P.S I know I am not supposed to use attachment but there are no way for me to input the table in a clean way... same for the logic circuit drawing. Would anyone mind helping me?

1. Homework Statement

## Homework Equations

AND gates require both input to be True to get a true ouput
NOT gates are just the opposite of what you input in them ( 1 -- > 0 and 0 --> 1)
OR gates require at least one input to be true to create a true output

## The Attempt at a Solution

I can't seem to understand why the answer key uses 4 AND gates with 3 output. Like the one below :

It just seems very... weird that there are only 4 a inputs where as in the truth table there are 8 inputs in the truth table. Anybody can help me understand that?

## Answers and Replies

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berkeman
Mentor
Have you drawn a Karnaugh Map for that truth table? Can you share it with us? :-)

Oh, well I know how, I just didn't try because this was a set of problems before it was taught, but I'll do that right now. ^^

Mark44
Mentor
It just seems very... weird that there are only 4 a inputs where as in the truth table there are 8 inputs in the truth table.
There are four inputs in the truth table -- A, B, C, and F -- not eight.

Edit: Make that three inputs -- A, B, and C --and one output -- F.

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So I'm guessing the first thing to do is reduce the truth table either using theorems or karnaugh map right? ( hence why you asked)... If so then I got the following

FAB 00 01 11 10
C
0 0 1 0 1
1 1 0 1 0
and then I group together if I remember correctly and that allows me to cancel the input that "changes" if the input is the same ( I don't know if I'm clear? :/). But none of them are similar.

Edit: Sorry I didn't express myself right... I meant 8 possibilities out of 3 inputs ( 2^3)
Edit2: Can't seem to format this table right ughhhh

berkeman
Mentor
Edit2: Can't seem to format this table right ughhhh
Try using the "code" tags to preserve spaces for formatting. Like this:

Code:
A B C D
0 1 0 1

Code:
AB      00  01  11  10
C
0          0   1   0   1
1          1   0   1   0
Thanks!!

berkeman
Mentor
Wow, doesn't look like there are any simplifications. That's why there are 4 separate minterms that you OR together to get the output.

NascentOxygen
Staff Emeritus
Science Advisor
@MarcL Has your question now been answered?

As an aside, if you were allowed to use any gates of your choosing, you'd just need a pair of 2-input exclusive-ORs.

F = A ⊕ (B⊕C)

berkeman
Mentor
F = A ⊕ (B⊕C)
Nice! Too bad he can't use XORs. I'll remember that trick! :-)

LCKurtz
Science Advisor
Homework Helper
Gold Member
Edit2: Can't seem to format this table right ughhhh
You can do nice K map tables in Latex:$$\begin{array}{|c|c|c|c|c|} \hline C|AB & 00 & 01 & 11 & 10\\ \hline 0&0&1&0&1\\ \hline 1 & 1 & 0 & 1 & 0\\ \hline \end{array}$$

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