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.

 

In one of my textbooks it says:
A+A=1
and
A1=A

So your A(BC+BC)=A(1)=A

 

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, ...

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.

 

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)

 

In one of my textbooks it says:
A+A=1
and
A1=A

So your A(BC+BC)=A(1)=A

@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.

 

Have you tried Karnaugh maps?
It might be easier to simplify with them.