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hw12_soln

# hw12_soln - ECE3060 Homework#@4:30pm November23,2006...

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ECE3060 November 23, 2006 Homework #12 due Thursday November 30 @ 4:30pm       150 points Solutions 1. (35) Consider the following state machine: Input Current State Next State Output 0 1 S1 S1 S2 S4 1 0 0 1 S2 S2 S1 S4 1 0 0 1 S3 S3 S5 S2 0 1 0 1 S4 S4 S2 S3 0 1 0 1 S5 S5 S3 S1 0 1 0 1 S6 S6 S2 S4 0 1 a. (5) Draw the state transition diagram. s4 s6 s2 s1 s3 s5 0/1 0/1 1/0 1/0 0/0 0/0 0/0 0/0 1/1 1/1 1/1 1/1

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b. (25) Minimize the state machine using the state minimization algorithm taught in lecture.  Show exactly how each step is reduced.  Skipping any steps will lose points (even if you have the correct answer; in other words, points will be assigned for correct execution of the algorithm at each step in addition to obtaining the correct final result). group states together if the outputs are the same for any input: П 1  = {{S 1 , S 2 }, {S 3 , S 4 , S 5 , S 6 }} now consider if the next states belong to the same block for any input. split {S 3 , S 5 } and {S 4 ,S 6 } because outputs are in different blocks: П 2  = {{S 1 , S 2 }, {S 3 , S 5 }, {S 4 ,S 6 }} split {S 4 } and {S 6 } because outputs are in different blocks: П 3  = {{S 1 , S 2 }, {S 3 , S 5 }, {S 4 }, {S 6 }} now more possible splitting: П 4  = П 3   c. (5) Redraw the reduced state transition diagram. Input
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hw12_soln - ECE3060 Homework#@4:30pm November23,2006...

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