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I'm very new to engineering/circuit design/programming and I could use some help simplifying this logic gate: z = A.B.C + A.B'.C' + A'.B'.C + A'.B'.C'.

I tried a whole bunch and came up with:

z = A.C + B'.C'

but the truth table is off.

I could use any assistance you have to offer, thanks.

mcftdhorappusswrtvo
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  • This question appears to be off-topic because it does not include any attempts at solving the question, and further, is for finding a solution to homework. – max_ Sep 09 '14 at 22:42

2 Answers2

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Truth table:

A  B  C  Z
0  0  0  1
0  0  1  1
0  1  0  0
0  1  1  0
1  0  0  1
1  0  1  0
1  1  0  0
1  1  1  1

Using just AND/OR/NOT:

Z = A'B' + A(BC + B'C')

If XOR is also allowed:

Z = A'B' + A(B ^ C)'
Paul R
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0

z = A.B.C + A.B'.C' + A'.B'.C + A'.B'.C'

Note that A.B'.C' + A'.B'.C' can be simplify to B'.C'

Then

A.B.C + A'.B'.C can be simplify to C(AB + A'B') and (AB + A'B') is XNOR

Therefore

Z= B'C'+C(A XNOR B)

Luo Sen
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