suppose that the state machine is a single input w and the output is different
How to minimize
First we split 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 different 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 variables
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