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# Class Note for ECE 474A at UA 2

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This 4 page Class Notes was uploaded by an elite notetaker on Friday February 6, 2015. The Class Notes belongs to a course at University of Arizona taught by a professor in Fall. Since its upload, it has received 14 views.

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Date Created: 02/06/15

PRACTICE PROBLEMS 8 Lecture 11 12 10 Fill in the following table XM XO What does canonical mean Provide two canonical representations ofF a b c bc Using only muxes build a circuit to perform a F A NAND B b F A B C Which of the following circuits are functionally equivalent to F a xor b A A B A B I B A AB 1 AB 1 F 1 F A F B F A39B F o 1 A A AB AB 0 AB 8 b C d 6 Using the Shannon Expansion Theorem expand Fa b c ac ab c b with respect to a Variable a b Variable b c Variable c Convert F a xor b xor c into aBDD using the variable ordering a S b S c Convert Fa b c d a bc d a bcd b d to its corresponding BDD representation using the variable ordering alt b lt c lt d Be sure to reduce the BDD if possible Convert Fa b c d ab a bc abc d to its corresponding BDD representation Use the variable ordering a b S c S d Given F abc bc d b d which ofthe following variable orderings is best to implement a ROBDD a Variable ordering d lt c lt b lt a b Variable ordering b lt c lt alt d Determine the equation represented by the BDD below 11 Determine the equation represented by the BDD below 12 Convert the following BDD into an ROBDD using the variable ordering A lt B lt C 13 Convert the following BDD into an ROBDD using the variable ordering C lt A lt B 14 Let Fad Gcd Hab and IFGF 39 H a Build a BDD for F G and H Then composed the BDD forI by iteratively connecting the previously created BDDs b Using the ITE algorithm create a BDD for I c What are the benefits of using the ITE algorithm 15 16 17 18 19 Let Fabc Gc d Ha b ab and IFGF H Use the ITE algorithm to create a BDD forI Be sure to show the corresponding steps ofthe ITE algorithm and the resulting BDD Use the variable ordering a lt c lt b lt d Let Fabc cd a b c Use the ITE algorithm to create the corresponding BDD for F Be sure to show the corresponding steps of the ITE algorithm and the resulting BDD Use the variable ordering c lt a lt d lt b Encoding the FSM below using the encoding techniques speci ed below Inputs x bit Outputs 5 bit t bit u bit a Minimum bitwidth binary encoding b Onehot encoding c Output encoding inputs x bit outputs y bits Reduce the number of states for the FSM below by eliminating redundant states by using an implication table Draw the resulting FSM inputs x bit outputs y bits 20 Reduce the number of states for the FSM below by eliminating redundant states by using an implication table Draw the resulting FSM inputs M bit outputs N bits 21 Minimize the following state table using the partitioning approach Show the corresponding partitions you do not need to show the minimized FSM l 5 Out 5 Current Z Next State State P S T R T T R T R S Q R T 22 Using the FSM provided inputs in bit a Derive the equivalent state table Outputs out bit f b Utilizing the state table minimize the FSM ie partitioning approach be sure to show each step c Draw the minimized FSM out 0 out 0 23 Which ofthe following yields the optimal state encoding assignment mm X m x a Minimum bit width binary encoding A00 B01 C10 Outputs abc bit b Modified minimum bit width binary encoding A00 B01 C11 c Onehot d Output encoding 24 Given Fa b c ab a bc b c determine the optimal variable ordering 25 Describe how the optimal variable ordering can be found What is the complexity of your method

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