How to simplify boolean expression given kmap

Question

Can someone explain to me how to find the simplified boolean expression given the kmap below? kmap

I'm grouping the 1's in the upper left corner, top row, and wrap-around in the fourth column but am getting the expression w'x' + w'y' + x'yz' when I should be getting w' + x'yz'... what am I doing wrong?

Given the x (don't-care) parts of the table, you can describe the whole top 2 rows with just w', which will produce 1 as the output for both x cases. I don't know a mechanistic or algorithmic way to simplify truth tables to boolean expressions, but as a human, the top half is (or can be) all ones and the bottom half all zeros, except for one entry whose exact condition you can OR with w'. — Peter Cordes
– Peter Cordes, Commented Sep 26, 2024 at 5:15
@PeterCordes how are you getting the expression for the single 1? I am getting wx'yz' but should be getting x'yz' — moosemarrin
– moosemarrin, Commented Sep 26, 2024 at 18:56
We're ORing that with w', so we don't need to stop that expression from being true when w is false (that's the top two rows). — Peter Cordes
– Peter Cordes, Commented Sep 26, 2024 at 18:59

user11844224 · Accepted Answer · 2024-10-05 20:55:06Z

0

circle the biggest 1s blocks; there are 2. look at the variables that do not change and AND those; w' for first big block, wx'yz' for the small/"singlet" second one. Then OR these two together: w' + wx'yz'

answered Oct 5, 2024 at 20:55

user11844224

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