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.
     
    shyamamoneymohan likes this.
  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.
     
    shyamamoneymohan likes this.
  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'
     
Loading...