UCSB ECE 152A - EXAMPLE FINAL EXAM (9 pages)

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EXAMPLE FINAL EXAM



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EXAMPLE FINAL EXAM

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Pages:
9
School:
University of California, Santa Barbara
Course:
Ece 152a - Digital Design Principles

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Department of Electrical Computer Engineering University of California Santa Barbara ECE 152A Summer 2011 Shynk H O 21 EXAMPLE FINAL EXAM INSTRUCTIONS 1 This exam is open book and open notes 2 It consists of 4 problems and is worth a maximum of 100 points The problems are not of equal difficulty so use discretion in allocating your time Answer all questions in any order 3 Show your answers in the spaces and additional pages provided and use the back side of the exam pages if you need additional work space Show your reasoning and the essential steps clearly and concisely Last Name First Name 1 ECE 152A Summer 2011 1 MULTIPLEXERS AND DECODERS 25 points Consider the following function f x1 x2 x3 x4 X m 0 4 6 7 8 11 12 14 15 1 a Find the minimum sum of products SOP implementation for f using a Karnaugh map b Use Shannon s expansion theorem to rewrite the result in part a by expanding it in terms of x3 Sketch a circuit diagram that implements f using a 2 1 multiplexer c Starting with the result in part b use Shannon s expansion theorem to further expand f in terms of x4 Sketch a circuit diagram that implements f using a 4 1 multiplexer d Show how to implement a 4 16 decoder with inputs x1 x2 x3 x4 using two 3 8 decoders Then use this decoder along with six two input OR gates and one three input OR gate to implement f in part a Solution 2 ECE 152A Summer 2011 3 ECE 152A Summer 2011 2 STATE MINIMIZATION AND MACHINE CONVERSION 30 points Consider the following next state table for a Mealy machine with input x and output z present state A B C D E F G H x 0 E 0 A 1 C 0 B 0 D 1 C 0 H 1 C 1 x 1 D 0 F 0 A 1 A 0 C 0 D 1 G 1 B 1 a Use partitioning to generate a reduced state machine Hint The minimal Mealy machine has five states Use A B C D E to label the reduced set of states b Use an implication table to obtain the same set of reduced states Clearly indicate your steps Give the state table for the reduced Mealy machine c Convert the reduced Mealy machine to the corresponding



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