State minization

  • to reduce cost comlpexity

Partition Minimization Procedure

  • Definition

    • 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

aab00
bcd00
cef00
dba01
ecd00
fba01
  • 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
aab00
bbd00
dba01
  • Then with this simplified table we can turn it into an implementation with a flipflop
    • Implementation with jk flip flop