5e_Dense_State_Assignment_Slides

# We can apply the state assignment we can apply the

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Unformatted text preview: We can apply the state assignment • We can apply the state assignment rules to each pair of states in a state table and summarize the information in another mileage chart. We will see an example once we have studied each of the state assignment rules. Rule 2 Rule 2 Rule 2 Rule 2 If 1 and 2 are adjacent input codes If x 1 and x 2 are adjacent input codes, then r – 1 horizontal adjacent pairs will occur if δ (A, x 1 ) and δ (A, x 2 ) i d j t t t d receive adjacent state codes. What are we trying to find? The next states of a present state for adjacent input combinations. Rule 2 Rule 2 Rule 2 Rule 2 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 2 Rule 2 Rule 2 Rule 2 • State B’s next state for inpu State Bs next state for input x 1 x 2 = 00 is B. State B’s next state for input x 1 x 2 = 01 is C. • States B and C are therefore the next states of the same present state for adjacent input codes . • If states B and C receive adjacent codes, then we will obtain 2 dj t i f l i l i th adjacent pairs of logic values in the state variable Karnaugh maps, regardless of how the designer makes B and C adjacent . Rule 2 Rule 2 Rule 2 Rule 2 Continuing with the arbitrary state assignment from the previous example, let’s give state C the code y 1 y 2 y 3 = 101. State B already has the code y 1 y 2 y 3 = 111. The next state code of state 111 for input 00 is 111. The next state code of state 111 for input 01 is 101. We can enter this information into 01 is 101. We can enter this information into the Karnaugh maps: x 1 x 2 1 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 B 111 1 1 1 D 110 1 1 1 + + + y 1 + y 2 + y 3 + z 1 z 2 Rule 3 Rule 3 Rule 3 Rule 3 If δ (A ) = A and (B ) = B, or if If δ (A, x 1 ) A and δ (B, x 1 ) B, or if δ (A, x 1 ) = B and δ (B, x 1 ) = A, then r – 1 vertical adjacent pairs will occur if A d B i dj t t t if A and B receive adjacent state codes. What are we trying to find? Two states that both have themselves as their next states, or that both have each othe as their next states each other as their next states. Rule 3 Rule 3 Rule 3 Rule 3 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 3 Rule 3 Rule 3 Rule 3 • State A’s next state for inpu State As next state for input x 1 x 2 = 00 is A. State B’s next state for input x 1 x 2 = 00 is B. • States A and B therefore both go themselves for the same input ....
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• Summer '06
• JSThweatt
• Karnaugh map, Maurice Karnaugh, Rule Rule

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