State Assignment

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# State Assignment - PowerPoint PPT Presentation

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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Presentation Transcript
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
• 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
• 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

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

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

q2q1

q0

A

A

B

B

E

D

C

q2q1

q0

E

D

C

Good