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5e_Dense_State_Assignment_Slides

5e_Dense_State_Assignment_Slides - ECE 3504 ECE 3504...

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Unformatted text preview: ECE 3504 ECE 3504 Digital Design 1 Digital Design 1 Section 5e: Dense State Assignments The Design Proces The Design Proces The Design Process The Design Process I. Read the statement of the problem. A. Settle the requirements of the specification. B. Determine the appropriate model. II. Model the system. A Create a stat transition diagram A. Create a state-transition diagram. B. Create a state-transition table. III. Eliminate redundant states. IV. Make a state assignment. A. Apply Armstong’s method to obtain maximal adjacencies OR B. Use a one-hot code state assignment Realize the circuit V. Realize the circuit. A. Select the flip-flop type. B. Use the appropriate excitation table to derive logic equations. C. Draw the circuit diagram for the logic equations. D. Simulate the circuit to judge its effectiveness effectiveness. E. Evaluate the cost and speed of the realization. State Assignment State Assignment State Assignments State Assignments • Now that we have a minimal table Now that we have a minimal table, we must make a state assignment. • The circuit must have enough flip- flops to assign a unique code to each state. Dense State Dense State Assignments Assignments • To minimize the number of fli flop To minimize the number of flip flops , recall that n state variables are sufficient to generate 2 n different bi d binary codes. • Let x be the number of states in the minimal state table. In a “dense” state assignment, implementing the state machine requires r flip flops where requires r flip-flops, where r = ⎡ log 2 x ⎤ • ⎡ x ⎤ is the ceiling of x – the smallest integer greater than or equal to x . Dense State Dense State Assignments Assignments • Instead of making an arbitrary state Instead of making an arbitrary state assignment or haphazardly trying different assignments, we will use a t t th t t i t i i th strategy that tries to maximize the number of pairs of adjacent logic values in the Karnaugh maps that will produce the state and output equations. Our hypothesis is that maximizing • Our hypothesis is that maximizing the number of adjacent pairs of ones and zeros in the maps will tend to group those logic values together, thereby simplifying the logic equations. Dense State Dense State Assignments Assignments Both maps have the same numbers of Both maps have the same numbers of 1s and 0s, but the map on the right has a simpler implementation. Note th dj f it 1 the adjacency of its 1s. CD CD 00 01 11 10 00 01 11 10 0 0 1 0 0 0 1 0 AB AB 1 0 1 0 0 1 1 0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 10 1 10 1 Dense State Dense State Assignments Assignments • This method uses five quantitativ This method uses five quantitative rules. We will apply the rules to the minimized state table and use th t t th b f them to count the number of adjacent pairs of logic values that will occur in the Karnaugh maps if two states have logically adjacent state codes....
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