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Hello I have to simplify the first expression which is from a 7 segment Display assignment. upper case means it is a NOT so for example the first part ZYXW means NOT z AND NOT y AND NOT x AND NOT w. I hope that makes sense.

So the problem is i found the answer for the expression which simplifies to a = z + x + yw + YW however my simplification ends at a = zYX

bellow are the steps for my simplification, could someone identify the problem please.

a = ZYXW + ZYxW + ZYxw + ZyXw + ZyxW + Zyxw + zYXw + zYXW
a = ZYXW + ZYxW + ZYxw + ZyXw + ZyxW + Zyxw + zYX(w + W)
a = ZYXW + ZYxW + ZYxw + ZyXw + ZyxW + Zyxw + zYX(1)
a = ZYXW + ZYxW + ZYxw + ZyXw + ZyxW + Zyxw + zYX.1
a = ZYXW + ZYxW + ZYxw + ZyXw + ZyxW + Zyxw + zYX

a = ZYXW + ZYxW + ZYxw + ZyXw + Zyx(W + w) + zYX
a = ZYXW + ZYxW + ZYxw + ZyXw + Zyx(1) + zYX
a = ZYXW + ZYxW + ZYxw + ZyXw + Zyx.1 + zYX
a = ZYXW + ZYxW + ZYxw + ZyXw + Zyx + zYX

a = ZYW(X + x) + ZYxw + ZyXw + Zyx + zYX
a = ZYW(1) + ZYxw + ZyXw + Zyx + zYX
a = ZYW.1 + ZYxw + ZyXw + Zyx + zYX
a = ZYW + ZYxw + ZyXw + Zyx + zYX

a = ZYW + Zw(xY + Xy) + Zyx + zYX
a = ZYW + Zw(x.1 + X.1) + Zyx + zYX
a = ZYW + Zw(x + X) + Zyx + zYX
a = ZYW + Zw(1) + Zyx + zYX
a = ZYW + Zw.1 + Zyx + zYX
a = ZYW + Zw + Zyx + zYX

a = Z(YW + w + yz) + zYX
a = Z(Y.1 + yz) + zYX
a = Z(Y = yz) + zYX
a = Z(z) + zYX
a = Z + z + zYX
a = 1 + zYX
a = zYX
user2839999
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1 Answers1

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Hey I think this exercise is for using Karnaugh Maps. With those its quite simple. Just look here: Karnaugh Map Wiki

First you create a truth table, like the one at the start of this tutorial. The 16 rows represent all combinations of your 4 variables. You get the result of a row, by comparing it to your function.

So 0 0 0 0 is equivalent to ZYXW and the solution would be 1 because ZYXW is in your function.

0 0 0 1 would be ZYXw which is not in your function, so the solution is 0.

0 0 1 0 would be ZYxW which is in your function, so the solution is 1.

Do this for all 16 rows. Then go ahead like in the Tutorial.

Baider
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  • Welcome to Stack Overflow, and thank you for answering. The trouble with link-only answers is they tend to become invalid over time. It would improve this answer if you could show the user of a K-map in the context of the question. – Wayne Conrad Jan 11 '14 at 14:43
  • We haven't went through that yet : / – user2839999 Jan 11 '14 at 14:44