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I really wonder why my method is wrong. Could you explain step-by-step and why my methods wrong. Drawings includes just one time isn't it enough for simplification ?

First boolen expression: $$ F = A'B'C'D' + A'B'C'D + A'B'CD + A'B'CD' + A'BC'D + A'BCD + ABC'D + ABCD + AB'C'D' + AB'C'D + AB'CD + AB'CD' $$ enter image description here

my result: $$ C'D + B'D + AB' + BD $$

Second boolean expression : $$ F = A'B'C'D + A'BC'D' + A'BC'D + A'BCD' + ABC'D' + ABC'D + ABCD' + AB'C'D' + AB'C'D + AB'CD + AB'CD' $$ the other one

enter image description here

my second result: $$ BD' + C'D + AB' $$

NewCoder
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    Your method could be right, depending on what boolean expressions you came up with from your pictures. I would suggest writing them. – parsiad Apr 09 '15 at 17:23
  • I added my results but when I check both of them wrong. Actually, my grouping method wrong. @par – NewCoder Apr 09 '15 at 17:38

1 Answers1

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kmap

You have 12 terms and only 11 1's. You missed the 1st term on second row.

Second Kmap and answer is correct.

Edit... You say: $$F(ABCD) = AB′ + C′D + BC′ + BD′$$ is the correct answer for the second kmap.

Consensus Law says $X Y + X'Z + Y Z = X Y + X'Z$.

So rearranging to make it easier to see: $DC′ + D′B + C′B = DC′ + D′B$.

$BC'$ is redundant.

If you include $BC'$, you must also include $AD'$. It's just as redundant. $$BD′ + B′A + D'A = BD′ + B′A$$

The only correct answer for kmap 2 is: $$F(ABCD) = AB′ + C′D + BD′$$

Community
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StainlessSteelRat
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  • thank you. but for second kmap, right answer is showed $$ F(ABCD) = A B' + C' D + B C' + B D' $$ – NewCoder Apr 11 '15 at 07:18
  • The B'C term is redundant. A kmap will produce minimal solution. You could also add AD'. It is redundant too. The right answer is wrong. Show your kmap to prove your answer is correct. – StainlessSteelRat Apr 11 '15 at 13:10