# Beginner question about logic simplification

Discussion in 'Homework Help' started by Mcftdhorapusswrtrvocm, Sep 27, 2014.

1. ### Mcftdhorapusswrtrvocm Thread Starter New Member

Sep 27, 2014
1
0
Hello there!
I need some help with simplification. We were given an equation and told to build the circuit out of it, but I can't simplify the function any more and it seems like way too much to build as is.

Ʃ m(0,1,3,5,6,9,10,15) + d(8,14)

and the truth table from that is:
D C B A - Z
0 0 0 0 - 1
0 0 0 1 - 1
0 0 1 0 - 0
0 0 1 1 - 1
0 1 0 0 - 0
0 1 0 1 - 1
0 1 1 0 - 1
0 1 1 1 - 0
1 0 0 0 - x
1 0 0 1 - 1
1 0 1 0 - 1
1 0 1 1 - 0
1 1 0 0 - 0
1 1 0 1 - 0
1 1 1 0 - x
1 1 1 1 - 1

I simplified the equation to:

A ( B C + B C ) + D ( B C + B C ) + C ( A XOR D ) + A B D

So that final function leaves me with 12 gates, and that seems like way too much for my first project, and I feel like there must be some way to simplify it but everything I've tried doesn't work. Once I was told that ( B C + B C ) could become ( B XNOR C) but that doesn't work or make sense.
here's a drawing:

And if you have any tips on how to put this all into an actual circuit, any help would be much appreciated. It just doesn't make any sense to me yet. I'll probably end up going to the teacher for help on Monday, but that's when the class is and I'm supposed to have it finished for the class.
Thanks for any help you can offer.

2. ### shteii01 AAC Fanatic!

Feb 19, 2010
3,514
514
In one of my textbooks it says:
A+A=1
and
A1=A

3. ### LDC3 Active Member

Apr 27, 2013
920
160
It seem to me that A ( BC + BC ) + D ( BC + BC ) would be equivalent to ( A + D )( BC + BC ). In which case, you could use 9 gates.

4. ### Papabravo Expert

Feb 24, 2006
10,340
1,850
Looking at the truth table you observe that there eight products that produce a 1 and six products that produce a 0 and two that produce a don't care. You have implemented a canonical SOP (Sum of Products), but you could have chosen to implement the equally valid POS (Product of Sums)

5. ### arivvu New Member

Sep 7, 2012
9
0
@shteii01 and @LDC3
i think he (thread starter) mentioned ([B' and C'] or [B and C]) it is not ([B and C]' or [B and C]). both will give different result, if it is first case result will not be 1 always.

6. ### jjw Member

Dec 24, 2013
174
32
Have you tried Karnaugh maps?
It might be easier to simplify with them.