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I am new to Karnaugh maps and I would like to find out how I can go about this the data is correct but maybe the layout of this table is not correct, there are four states s0s1s2s3 and the inputs are B and Y where the next stage or state is noted by S1' and S0'the X are there because the diagram had a Y' hence not Y and B is independent of it. I am trying to find the SOP(sumofproducts)binary form of this truth table. Thank you any help will be appreciated

  • \$\begingroup\$ What does this mean -> X are there because the diagram had a Y' hence not Y and B is independent of it. \$\endgroup\$
    – user28910
    Commented Jun 8, 2020 at 18:36

1 Answer 1


This looks like a homework problem, and we don't just hand out homework solutions here. But I will give you some hints to get started.

You have named the states (S0, S1, etc.) the same as your state variables (S0 and S1). That is incredibly confusing, so pick different names for the states.

You need 2 Karnaugh maps, one for each of the "next state" bits. The input signals for the Karnaugh maps will be the two state variables (the "current state" bits) as well as the two input variables.

So, create your two, four-variable K maps and go through the usual procedure to find your optimized SOP implementation.

  • \$\begingroup\$ Thank you for your advice, I did not notice those names so I will change it. I tried to fill in the maps so the inputs are S1 S0(States)B Y (variables) for both maps. However I have just 9 lines and I looked into many K-map examples they are all from 0000 to 1111 (16 lines) and the next state they do not have enough data what do i do with this do i just put an X there? I tried to look into a lot of tutorials and I just cannot understand, Thank you. \$\endgroup\$
    – AmberDot
    Commented Jun 8, 2020 at 17:22
  • \$\begingroup\$ What do you mean by "they do not have enough data"? You must create a separate K map for each bit of the "next state"...so two different K maps in your case. \$\endgroup\$ Commented Jun 8, 2020 at 17:31
  • \$\begingroup\$ I mean that I have only 8 lines for each 'next state' and the template of truth tables for e.g ABCD k maps are always 16 lines 0000,0001,0010... 1111 where you enter the output data which in this case are s0' and for second one s1' \$\endgroup\$
    – AmberDot
    Commented Jun 8, 2020 at 17:58
  • \$\begingroup\$ @AmberDot: "spell out the X lines": for every X, create one line with 0 and one with 1 - there are your 16 lines. \$\endgroup\$
    – greybeard
    Commented Dec 6, 2022 at 20:23

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