Electronic – Using don’t cares to reduce a function

boolean-algebrakarnaugh map

We have the function: f = p'c' + pb' + qc

With satisfiability don't cares given by SDC = {pb, q'b', qbc, q'*c'}

The K-map for the function is :

      \ b'*c' | b'*c | b*c | b*c'
p'*q' |   1   |  0   |  0  |  1
p'*q  |   1   |  1   |  1  |  1
p*q   |   1   |  1   |  1  |  0
p*q'  |   1   |  1   |  0  |  0

and using the "don't cares" in the k-map gives the unfilled k-map

      \ b'*c' | b'*c | b*c | b*c'
p'*q' |   X   |  X   |  0  |  X
p'*q  |   1   |  1   |  X  |  1
p*q   |   1   |  1   |  X  |  X
p*q'  |   X   |  X   |  X  |  X

Why does the book say that the minimized function is

f = p'c' + q

when the k-map indicates that the function should be

f = q

Did I mess up somewhere?

Best Answer

It has been pointed out that there may be a transcription error, and the consensus is that the problem as stated with my result is in fact correct.

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