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Unformatted text preview: Department of Electrical & Computer Engineering ECE 152A University of California, Santa Barbara 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 ( x 1 ,x 2 ,x 3 ,x 4 ) = summationdisplay 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 x 3 . Sketch a circuit diagram that implements....
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