Have I simplified this Min-term Correctly?

Question

I have got two different solutions and I would like to know if they are correct, I would be very grateful if you could let me know if they are correct or what I can do to correct them.

Solution 1

  A'BC'D' + AB'C'D' + AB'CD' + ABC'D +ABCD'
  A'BC'D' + AB'D'(C'+C) + ABC'D + ABCD'
  A'BC'D + AB'D'(1) + ABC'D + ABCD'
  BC'(A'D' + AD) AB'D'+ABCD'
  AB'D' + BC' + ABCD'
  A(B'D'+ BCD') + BC'
  AD'(B'+ BC) + BC'
  AD'C + BC'
  ABC'D'

Solution 2

  A'BC'D' + AB'C'D' + AB'CD' + ABC'D +ABCD'
  A'BC'D' + AB'D'(C'+C) + ABC'D + ABCD'
  A'BC'D' + AB'D'(1) + ABC'D + ABCD'
  A'BC'D' + AB'D' + AB(C'D + CD')
  A'BC'D' + AB'D' + AB(1)
  AB'D' + AB + A'BC'D'
  A(B'D+B) + A'BC'D'
  A(BD) + ABC'D')
  ABD + A'BC'D'
  B(AD + A'C'D')
  B(AC'D)
  ABC'D

Again, I will be very grateful if anyone can confirm it is correct or help me simplify it correctly.

Thanks.

score 1 · Answer 1 · answered Dec 08 '15 at 04:51

I see several mistakes like $$x\overline y + \overline x y \ne 1$$ $$x y + \overline x \overline y \ne 1$$ $$\overline x + x y \ne y$$ And so on... I would do this way

A'BC'D' + AB'C'D' + AB'CD' + ABC'D +ABCD'

= A'BC'D' + AB'(C'+C)D' + ABC'D +ABCD'

= A'BC'D' + AB'D' + ABC'D +ABCD'

= A'BC'D' + A(B'+BC)D' + ABC'D

= A'BC'D' + A(B'+C)D' + ABC'D

= A'BC'D' + AB'D' + ACD' + ABC'D

I don't think it can be further reduced..

Have I simplified this Min-term Correctly?

1 Answers1