Quick simplification check

Discussion in 'Homework Help' started by Gotmilk0112, Apr 21, 2013.

  1. Gotmilk0112

    Thread Starter Member

    Mar 24, 2013
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    Need a quick simplification check for simplifying boolean variables into XOR statements.

    P1, P2, P3, P4, B are just normal variables, in this case of simplification.

    Ja = P1•P2'•P3'•P4'•B' + P1'•P2•P3'•P4'•1 + P1'•P2'•P3•P4'•B' + P1'•P2'•P3'•P4•B'
    = (P1 xor P3 xor P4) • B' + P1'•P2•P3'•P4'•1

    Ka = P1•P2'•P3'•P4'•1 + P1'•P2•P3'•P4'•B' + P1'•P2'•P3•P4'•1 + P1'•P2'•P3'•P4•B'
    = (P2 xor P4) • B' + (P1 xor P3) • 1

    Is this correct? I'm not sure exactly how to simplify into XOR statements with so many variables like this.
     
  2. WBahn

    Moderator

    Mar 31, 2012
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    The beautiful thing about manipulating logic expressions is that you can always verify whether or not they match by generating the truth tables for both sides and seeing if they agree.

    Do they?

    Before doing the full up table, do some sanity checks. For instance, for Ka, what will your simplified expression result in for the case of B=1, P1=1, P2=1, P3=0, P4=0 ? What should Ka be for this set of inputs?
     
  3. Gotmilk0112

    Thread Starter Member

    Mar 24, 2013
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    Uh...I don't know what Ka would be for that set of inputs. I don't even know where to start, there.
     
  4. WBahn

    Moderator

    Mar 31, 2012
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    Let's take it one step at a time.

    For that set of inputs, would (P2 xor P4) be a 0 or a 1?
     
  5. Gotmilk0112

    Thread Starter Member

    Mar 24, 2013
    32
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    (1 xor 0) = 1
     
  6. WBahn

    Moderator

    Mar 31, 2012
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    Good.

    Now will B' be a 0 or a 1?
     
  7. Gotmilk0112

    Thread Starter Member

    Mar 24, 2013
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    1' = 0

    Where exactly is this headed?
     
  8. WBahn

    Moderator

    Mar 31, 2012
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    Good.

    You said, "I don't know what Ka would be for that set of inputs. I don't even know where to start, there." I am just taking you at your word and walking you through it step by step. I'm hoping that, at some point, something will click and you will grab the ball and run with it.

    Now, is (P2 xor P4) * B' a 0 or a 1?
     
  9. Gotmilk0112

    Thread Starter Member

    Mar 24, 2013
    32
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    1 * 0 = 0

    10char
     
  10. WBahn

    Moderator

    Mar 31, 2012
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    I don't know if "10char" was supposed to mean anything or is just orphaned text that didn't get deleted.

    So fine. Now let's move to the second term.

    Will (P1 xor P3) be a 0 or a 1?
     
  11. Gotmilk0112

    Thread Starter Member

    Mar 24, 2013
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    1 xor 0 = 1

    I still don't see where this is going.
     
  12. WBahn

    Moderator

    Mar 31, 2012
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    Good.

    Now, will (P1 xor P3) * 1 be 0 or 1?

    The fact that you don't see where this is going when the goal has been clearly stated that we are trying to find out what Ka is for a particular set of inputs for both the original expression and your proposed simplification of it is quite troubling. But, perhaps something will still click.
     
  13. Gotmilk0112

    Thread Starter Member

    Mar 24, 2013
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    I don't see how this is helping me simplify the sets of variables.

    But if you insist...

    1 * 1 = 1
     
  14. WBahn

    Moderator

    Mar 31, 2012
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    Good, so now, is

    Ka = (P2 xor P4) • B' + (P1 xor P3) • 1

    a 0 or a 1 for this set of inputs?
     
  15. Gotmilk0112

    Thread Starter Member

    Mar 24, 2013
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    1 * 0 + 1 * 1 = 1

    I seriously don't see how this is helping. Can we just get to the point already?
     
  16. WBahn

    Moderator

    Mar 31, 2012
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    You asked if your simplification was correct.

    I told you to check a particular set of inputs in both the original expression and your simplified expression. You said that you didn't know how to do that. So we are walking through evaluating both expressions for that set of inputs step by step. If you want to move faster, then by all means evaluate the expressions for that set of inputs and we can have an answer as to whether your simplification is correct.

    But since you haven't done that, I have no choice but to continue to take you at your word that you have no idea how to evaluate these expressions.

    So, at this point, we have that YOUR expression yields a 1 for that particular set of inputs.

    Let's turn our attention to the original expression. There fore four terms. Let's take them one at a time. The first terms is

    P1•P2'•P3'•P4'•1

    Can you evaluate this for the stated set of conditions, or do we need to break it down further? If not, then will this yield a 0 or a 1?
     
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