Electronic – Karnaugh Map race conditions with don’t cares

boolean-algebrakarnaugh maplogic-hazardrace condition

Karnaugh maps show race conditions as adjacent minterms that are not covered in the same implicand. Take the following example:

We have race conditions when moving from the blue implicand to the green one, and the blue implicand to the red one (wrapping around the top).

My question is this: would this still apply if the adjacent '1' is a don't care, i.e. an 'X'? In this case, let's change the 1 in minterm AB'CD' (bottom right) to an 'X'. Would this still pose a potential race condition with minterm ABCD'?

Best Answer

Yes it would.

If you experience the transition A'B'CD' → AB'CD' → ABCD', the output should show 0 → X → 1, which is either 0 → 0 → 1 or 0 → 1 → 1. In both cases, you should see a single 0 → 1 transition in the output.

But with your example, you might see 0 → 1 → 0 → 1 in the output: you have a race condition.

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Electronic – Minimizing Karnaugh map

Assuming that \$\Phi\$ is the same as X (don't care), I would make the following corrections:

JA = ¬B ¬C ¬D
Here you covered a 0 that you shouldn't, so you have to make a smaller minterm.

KA = D
Here you can make a bigger minterm because the 2*2 are above the minterm only contains don't cares.

KC = ¬D
Again, you can meg a bigger minterm. You don't have to add C because the first column only contains don't cares and ¬D covers the first and the last column.

Electronic – Question on Logic circuit and Karnaugh Map

 B   !B    C   B??C
---  ---  ---  ----
 0    1    0    1
 0    1    1    1
 1    0    0    0
 1    0    1    1
 0    1    0    1
 0    1    1    1
 1    0    0    0
 1    0    1    1

Do you see it now?

Best Answer

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Electronic – Minimizing Karnaugh map

Electronic – Question on Logic circuit and Karnaugh Map

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