# How to fill in k-map with values from an finite state machine table?

I'm struggling to understand how I am supposed to fill in this k-map with the help of this finite state machine table?

I understand that q1q0 shows the present state but I don't understand how I am supposed to figure out what the next state is and fill in the k-map. In this table b not-b, a and not-a are used to describe the next state which I have not seen done before and there are no examples that provide an explanation as to how one finds the next state when given b and a and not numbers like 0 and 1 which is a lot easier to udnerstand.

Can someone explain what the next state from 00 is and also explain how you came to this conclusion so I can do the rest.

• Does this answer your question? State Table & Karnaugh-map for Finite State Machine Jun 17, 2023 at 23:28
• No it does not. I have edited the question to be more specific in what I need help with Jun 17, 2023 at 23:39
• @Dyson Did you do a sanity check? (First thing I tend to do, I guess.) For example, validate that $\left(\overline{b}+a\right)+b\overline{a} = 1$ (state 00) and then do the same for each and every one of the states with their outgoing arrow logic? I would tend to assume it passes such checks. But I just wonder if you double-checked the problem, already. Jun 18, 2023 at 0:58
• @Dyson For the first row, state 00, three of the four possibilities go to state 11. The remaining possibility goes to state 10. Is it then too difficult to fill out that row? Jun 18, 2023 at 2:26

b and a are the arrow labels from the state diagram.
picking the top state of 01 as an example.

Find the row for 01: the second one.
For each input state, enter the next machine state as indicated by the arrow labels into the table:
"The a inputs" go to the "middle" columns, the ¬a go to the outer.

      q₁q₀⁺
\ 00 01 11 10  ba
00
01 00 11 11 00
11
10
q₁q₀


the following tables are just the left one split for q₁ and q₀ for "Karnaugh grouping".

      q₁q₀⁺                q₁⁺             q₀⁺
\ 00 01 11 10  ba     00 01 11 10     00 01 11 10
00 11 11 11 10          1  1  1  1      1  1  1  0
01 00 11 11 00          0  1  1  0      0  1  1  0
11
10
q₁q₀

• Thank you! I got confused by the b and a since I'm used to dealing with 0 and 1. But your example helped me understand. Jun 18, 2023 at 16:22