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Homework Help: Boolean Algebra problem

  1. Apr 21, 2015 #1
    1. The problem statement, all variables and given/known data
    Minimize the following using boolean identities
    1. AB'CD+(ABC')'+ABCD'

    2. Relevant equations
    Identity 1A=A 0+A = A
    Null (or Dominance) Law 0A = 0 1+A = 1
    Idempotence Law AA = A A+A = A
    Inverse Law AA = 0 A+A = 1
    Commutative Law AB = BA A+B = B+A
    Associative Law (AB)C = A(BC) (A+B)+C = A+(B+C)
    Distributive Law A+BC = (A+B)(A+C) A(B+C) = AB+AC
    Absorption Law A(A+B) = A A+AB = A
    DeMorgan's Law (AB) = A+B (A+B) = A B

    3. The attempt at a solution
    I'm going to use lower case letters now.


    --> f=a'+b'+c

    Do this look correct? If so is there a shorter way to minimize it? Is there a way to minimize without using DeMorgan's theorem at the top? Thanks

  2. jcsd
  3. Apr 22, 2015 #2
    I didn't read you calculation, but it seem clear that a and c must both be true, sp your final answer must be wrong. Try actually thinking about the logic, & afterward pick the formal identities to back up your intuition
  4. Apr 22, 2015 #3


    User Avatar

    Staff: Mentor

    Impressive. I got the same answer via the K-map. :smile:
  5. Apr 22, 2015 #4
    sorry my mistake, i misread the question. your answer is correct. i would expand the middle term, and then show that it dominates.
  6. Apr 22, 2015 #5
    Great. Thank you. I found a much quicker way.

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