suppose that the state machine is a single input w and the output is diffrient
How to minimize
First we splite the outputs with 1 and 0
once we split it we write the 0 outputs as “0-successor” and 1s as “1-successor” but there are diffrent ones, we have to take the next state of the inputs not the actual outputs
Row elimination
Definition
When we have a table or a system of the varibles
we would look for the tables that have the same output and inputs, then we can cancel them and replace them with each other as they equal eachother
Example
a
a
b
0
0
b
c
d
0
0
c
e
f
0
0
d
b
a
0
1
e
c
d
0
0
f
b
a
0
1
We can tell that b=e, and d=f
then we can simplify it further by making the original terms equal the ones that have the same output, like b/c, c=b, d=d
a
a
b
0
0
b
b
d
0
0
d
b
a
0
1
Then with this simplified table we can turn it into an implementation with a flipflop