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**Unformatted text preview: **The adjacent pairs that the rules • The adjacent pairs that the rules predict depend only on whether or not the two states in question have logically adjacent codes. They do not depend on what codes are assigned. Notation Notation Notation Notation • Let A, B, C et ., be distinct state of Let A, B, C, etc ., be distinct states of the table, as represented by its rows . • Let x 1 and x 2 be distinct input combinations of the table, as represented by its columns . • δ (A, x 1 ) is the next state of state A for input x 1 . • λ i (A,x 1 ) is the i th Mealy output of state A for input x 1 . • If λ (A,x ) = 01, then λ (A,x ) = 0 If λ (A,x 1 ) 01, then λ 1 (A,x 1 ) 0, and λ 2 (A,x 1 ) = 1. • λ i (A) indicates the i th Moore output of state A. Rule 1 Rule 1 Rule 1 Rule 1 If δ (A ) = δ (B ), then vertical If δ (A, x 1 ) δ (B, x 1 ), then r vertical adjacent pairs will occur if A and B receive adjacent state codes. What are we trying to find What are we trying to find? Two states that have the same next state. Rule 1 Rule 1 Rule 1 Rule 1 Consider the partia state table Consider the partial state table shown below: x 1 x 2 00 01 11 10 A A / 11 E / 10 A A / 11 E / 10 B B / 01 C / 11 C C / 1 r = 3 D B / 1 E A / 1 1 NS / 1 2 NS / z 1 z 2 Rule 1 Rule 1 Rule 1 Rule 1 • In the previous state table, state B’s In the previous state table, state Bs next state for input x 1 x 2 = 00 is B. State D’s next state for input x 1 x 2 = 00 i l B = 00 is also B. • Therefore, states B and D have the same next state for the same input . • If states B and D receive adjacent codes, we will obtain 3 adjacent i f l i l i t h t t pairs of logic values in the state variable Karnaugh maps, regardless of how B and D are made adjacent . Rule 1 Rule 1 Rule 1 Rule 1 Suppose that an arbitrary state assignment gives state B the code y 1 y 2 y 3 = 111 and gives state D the code y 1 y 2 y 3 = 110. The next state code of state 111 for input 00 is 111. The next state code of state 110 for input 00 is also 111. We can enter this information into the Karnaugh maps into the Karnaugh maps: x 1 x 2 y 1 y 2 y 3 00 01 11 10 00 01 11 10 00 01 11 10 00 01 11 10 00 01 11 10 000 001 011 010 100 101 111 What if the states are assigned different 110 y 1 + y 2 + y 3 + z 1 z 2 adjacent codes? Applying the State Applying the State Assignment Rules Assignment Rules • Since the numbe of adjacent pairs Since the number of adjacent pairs does not depend specifically on the state codes that we assign, we can t th b f dj t i count the number of adjacent pairs that occur for each of the rules if a given pair of states receives adjacent state codes before we actually make the assignment....

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- Summer '06
- JSThweatt
- Karnaugh map, Maurice Karnaugh, Rule Rule