I have the following state transition table:

enter image description here

A, B - current states of two D flip flops

A+, B+ - next states of the two D flip flops

X1, X2, X3 - inputs to the current states

There are don't care conditions in inputs X1, X2 and X3.

I am trying to make a K-map for A+ using four variables A, X1, X2 and X3. I have dealt with don't cares in the output. But, I don't know how to deal with don't cares when they are on the input side.

How to deal with input don't care conditions ?

(I somehow tried to solve and got the answer: A+ = A'*X2'. Answer key has something else the answer. My state transition table is same as the one given in the answer key. So, I am sure that my state transition table is correct. I am sure that I am making mistakes in building K-maps from table as I don't know to incorporate input don't cares.)

  • \$\begingroup\$ The A+ K-Map needs to have 5 variables, A, B, X1, X2 and X3 \$\endgroup\$ Commented Nov 22, 2015 at 10:06
  • \$\begingroup\$ The B+ K-Map also needs 5 variables. The next state of both flops depends upon the current state of both plus the inputs. \$\endgroup\$ Commented Nov 22, 2015 at 10:57

1 Answer 1


In this case the input don't cares are quite simple. When you code each row into the K-Map you should code your desired output in cells that meet the input variable requirements. If a certain Xi is a don't care you have more places to fill in your outputs.

What I am trying to say is that you need to find all cells in the KMap that specifically satisfy the output ignoring inputs where there is a don't care.

Here are the direct fill outs in the K-Maps for A+ and B+. I'll leave it to you to perform the minimization steps.

enter image description here

  • \$\begingroup\$ @Micheal Karas Thank you very much! Although, some of the terms in my simplified expression are not matching with given answer, I got to know how to incorporate input don't cares. \$\endgroup\$
    – maverick
    Commented Nov 27, 2015 at 5:49

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