how to simplify this boolean algebra expression with only boolean algebra

Discussion in 'Homework Help' started by Maremare, Sep 12, 2019.

  1. Maremare

    Thread Starter New Member

    Sep 12, 2019
    3
    0
    I have to show that Y and Z are equal,

    Y = (~ABC) + (A~B~C) + (A~BC) + (AB~C) = (~ABC) + (A~C) + (A~B)

    But I don't know how to simplify this

    Z = (A+B+C) ( A+B+~C) (A+~B+C) (~A+B+C)

    How do i start?

    (with ~ i mean invert)
     
  2. WBahn

    Moderator

    Mar 31, 2012
    24,562
    7,700
    Don't worry about simplifying, just put both into the same standard form and see if they match.

    This might help: https://forum.allaboutcircuits.com/blog/boolean-logic-sop-and-pos-forms.583/
     
  3. Maremare

    Thread Starter New Member

    Sep 12, 2019
    3
    0
    okey thanks!
     
  4. Maremare

    Thread Starter New Member

    Sep 12, 2019
    3
    0
  5. WBahn

    Moderator

    Mar 31, 2012
    24,562
    7,700
    Consider if you are asked to show that the two expressions:

    (x+3)(x-9)

    and

    (x-3)² - 36

    are the same.

    Could you not expand each to get

    (x+3)(x-9) = x² + 3x - 9x - 27 = x² - 6x - 27

    (x-3)² - 36 = x² - 6x + 9 - 36 = x² - 6x - 27

    And since both expand to the same expression, conclude that the two original expressions are equivalent?

    Also, keep in mind that once you get them both to the same intermediate expression, you can always walk the process backwards and use that to convert one expression into the other explicitly.
     
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