# Need help in reducing boolean expression

#### Mujtaba60

Joined Oct 13, 2014
2
Hi everyone;
I am new and this is my first thread;
i need help in solving these 2 question

1) Reduce the following Boolean expressions to the minimum number of literals?
(A+C+D)(A+C+D')(A+C'+D)(A+B')

2) First take the complement and then reduce the expression to minimum literals possible:
B'D + A'BC' + ACD + A'BC

#### djsfantasi

Joined Apr 11, 2010
5,829
And what have you done so far? The way this works is you show what you have done and where you have gotten stuck, and we help from there. This is not the "homework done for you" forum.

#### Mujtaba60

Joined Oct 13, 2014
2
This is what i have done so far
2) B'D + A'BC' + ACD + A'BC
=B'D + A'B(C'+C) + ACD
=(B'D + A'B + ACD )
=(D(B'+AC)+A'B)'
=D'+B(A'+C')(A+B')
=D'+BA'A+A'B'B+ABC'+BB'C'
=D'+0+0+ABC'+0
=D'+ABC'

#### WBahn

Joined Mar 31, 2012
24,967
Are you familiar with Karnaugh Maps? If so, one way to check your work is to do the K-map for the problem.

If you aren't familiar with K-maps, then that's okay. You need to learn to do sanity checks. First, always make sure that you are actually answering the problem that was asked. The problem told you to first take the complement of the expression and it doesn't appear that you did that. But then your work claims that

B'D + A'BC' + ACD + A'BC = D'+ABC'

Does this make sense? The RHS says that the expression is true any time that D=0. Does that agree with the LHS?

In looking for where you went wrong, I see that it appears that you took the complement on your fourth line. But you are explicitly claiming that all of the lines in your work are equal (that's what the equality sign means, isn't it?). That's why I assumed you were saying that the bottom line was supposed to be equal to the first line -- because that IS what you were saying. Don't be sloppy like that -- it's asking for all sorts of trouble.

But we can still ask a similar sanity question. Your last line says that the complemented expression is TRUE whenever D=0. That means that the original expression MUST be FALSE whenever D=0. Is that the case?

You left out several steps in going from your fourth line to your fifth. Don't leave those out -- if nothing else it makes if very hard for someone, say a grader, to follow your work and see where you went wrong and assign you the maximum partial credit that you've earned. In this case, it appears you did this mostly correctly, but you missed a grouping that is critical and that you probably would not have missed had you put all the major steps (I count four where you just have one) in writing -- and it would have been much easier for you to later identify the mistake once you knew the answer was wrong.

Hope that helps.

• Mujtaba60