5e_Dense_State_Assignment_Slides

Since moore outputs have no input dependence we do

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Unformatted text preview: • Since Moore outputs have no input dependence, we do not count the single occurrence of Rule 4 for each input . Instead, we only count it once. x 1 x 2 00 01 11 10 z 1 z 2 1 2 A A E 11 B B C 1 C C 10 r = 3 D B 1 E A 1 1 NS Rule 5 Rule 5 Rule 5 Rule 5 If A and B alread have adjacent state If A and B already have adjacent state codes, and if δ (A, x 1 ) = C and δ (B, x 1 ) = D, then r – 1¡vertical¡ dj t i ill if C d D adjacent pairs will occur if C and D also already have adjacent state codes. Wait! What? If the point of this exercise is to make a state assignment, how can we know a state assignment, how can we know at this point which states already have adjacent state codes? Rule 5 Rule 5 Rule 5 Rule 5 If A and B alread have adjacent state If A and B already have adjacent state codes, and if δ (A, x 1 ) = C and δ (B, x 1 ) = D, then r – 1¡vertical¡ dj t i ill if C d D adjacent pairs will occur if C and D also already have adjacent state codes. What are we trying to find? After making the assignment , two adjacent present state whose next adjacent present states whose next states are also adjacent . Rule 5 Rule 5 Rule 5 Rule 5 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 5 Rule 5 Rule 5 Rule 5 • Suppose that states A and B have Suppose that states A and B have already received adjacent state codes. • State A’s next state for input x 1 x 2 = 01 is E. State B’s next state for input x 1 x 2 = 01 is C. 1 2 • Therefore, states C and E are the next states of two states that are l d d j already adjacent . • If states C and E have already received adjacent state codes in our assignment, then we will obtain 2 additional adjacent pairs of logic values in the state variable values in the state variable Karnaugh maps. Rule 5 Rule 5 Rule 5 Rule 5 In our arbitrary state assignment, let’s give state E the code y 1 y 2 y 3 = 001. States A and B have adjacent codes. E and C are the next states of A and B respectively, and E and C also have adjacent codes. We would already have filled this information We would already have filled this information into the Karnaugh map as a result of the assignment. Let’s see what happens: 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 E 001 A 011 1 1 1 1 1 010 100 C 101 B 111 1 1 1 0 1 1 0 1 1 1 D 110 1 1 1 + + + y 1 + y 2 + y 3 + z 1 z 2 Applying the State Applying the State Assignment Rules Assignment Rules • Create a mileage chart for the Create a mileage chart for the reduced state table. Each box of the mileage chart compares the t t t th l ft d b tt two states on the left and bottom axes that meet at that box....
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  • Summer '06
  • JSThweatt
  • Karnaugh map, Maurice Karnaugh, Rule Rule

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