# need help to solve this boolean expression

Discussion in 'Homework Help' started by shyamamoneymohan, Jan 9, 2014.

1. ### shyamamoneymohan Thread Starter New Member

Jan 9, 2014
3
0
((A exor B) .c) wholebar

answer which i got from a web site is A bar B bar +AB +C bar

can any one please explain how this comes..

2. ### MrChips Moderator

Oct 2, 2009
12,447
3,363
Use De Morgan's Laws.

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3. ### WBahn Moderator

Mar 31, 2012
17,757
4,800
I would recommend adopting a cleaner, more common way of writing your expressions.

F = ((A XOR B)C)'

F = (A')(B') + AB + C'

First, expand the XOR into its full expression using only AND, OR, NOT.

The apply DeMorgan's.

An alternative is to consider the logic expression for the XNOR gate.

Finally, show your work for as far as you are able to get it. We will help you see the next step, we won't just show you how to do it.

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4. ### shyamamoneymohan Thread Starter New Member

Jan 9, 2014
3
0
thanks WBahn for the explanation. now i was able to solve it.

5. ### shyamamoneymohan Thread Starter New Member

Jan 9, 2014
3
0
- >> (a`b+ab`)`+c`

(a`b)`.(ab`)`+c`

(a`+b)(a+b`)+c`
that gives my answer --> ab+a`b`+c`

6. ### WBahn Moderator

Mar 31, 2012
17,757
4,800
Yep. That's the most fundamental way to approach it.

Another way to come at it at a somewhat higher level would be:

F = [ (a XOR b) c ]'

F = (a XOR b)' + c'

F = (a XNOR b) + c'

The XNOR gate is also sometimes called the equality gate (for two inputs only), so (a XNOR b) is true if both a and b are T or if both a and b are F.

F = (ab + a'b') + c'

F = ab + a'b' + c'