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State Assignment. During the design process, states are often denoted symbolically Some state assignments (choosing a binary representation of the state) result in simpler circuits than other state assignments Some simple guidelines avoid the worst state assignments. Rules for State Assignment.

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State assignment
State Assignment

  • During the design process, states are often denoted symbolically

  • Some state assignments (choosing a binary representation of the state) result in simpler circuits than other state assignments

  • Some simple guidelines avoid the worst state assignments


Rules for state assignment
Rules for State Assignment

  • Section 15.8 of Roth

  • 1) States which have the same next state for a given input should be adjacent

    • (adjacent means differing by a single bit in the state assignment= adjacent in a Karnaugh map)

  • 2) States which are the next state of a given state should be adjacent

  • To minimize the output equation: States which have the same output for a given input should be adjacent


Applying the rules for state assignment
Applying the Rules for State Assignment

  • Apply rule 1 first, then apply rule 2

  • Multiple requirements should be placed as groups of 4 or more on the Karnaugh map

  • State adjacencies which occur more than once should be give precedence


State Transition Table for a vending machine selling a 25 cent item

5 states need 3 f-f’s

How many flip-flops are required?

States which have the same next state should be adjacent Examine the columns

Rule 1: (D,E) (A,B,C,D,E)

States which are the next state of a given state should be adjacent Examine the rows

Rule 2: (A,B,C) (A,B,C,D) (A,C,D,E) (A,D,E) (A,E)


A cent item

B

E

D

C

Rule 1: (D,E) (A,B,C,D,E)

Rule 2: (A,B,C) (A,B,C,D) (A,C,D,E) (A,D,E) (A,E)

Rule 1: all 5 adjacent -- put them in a group of 4 with 1 adjacent

D must be adjacent to E

Rule 2: AC occurs 3 times, AD occurs 3 times, AE occurs 3 times

AB occurs 2 times, BC occurs 2 times, CD occurs 2 times

CE occurs 1 time

q2q1

q0

Note: if D and E are adjacent, A cannot be adjacent to both D and E


Good bad

q2q1 cent item

q0

A

A

B

B

E

D

C

q2q1

q0

E

D

C

Good/Bad

Good

Bad

Note that to confirm that “Good” is better than “Bad” would

require finding 6 (or 12) 5-variable minimum expressions


State Transition Table for a vending machine selling a 25 cent item

Minimizing the output equation:

States that have the same output for a given input should be adjacent.

For the vend/don’t vend: (ABCDE), (ABCD), (ABC), (ABCDE)

Conclusion: ABCD should be in a group of 4


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