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exam2_03 - Department of Electrical and Computer...

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Department of Electrical and Computer Engineering The Johns Hopkins University 520.137 Introduction to Electrical and Computer Engineering – Fall 2003 Examination II 1. There are 4 problems. You have 55 minutes . 2. Closed book. Closed notes. One 8 . 5 00 × 11 00 cheat sheet allowed. 3. Read the questions carefully. Make sure that you answer every question posed. 4. Express your final answer in the most compact and simplified form. 5. Justify all of your answers. 6. State all of your assumptions if necessary. 7. Show your work clearly, neatly, and precisely.
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I A binary representation that finds many applications in practice is Gray Code . This is simply a reshuffling of the traditional binary code with the property that any two consecutive numbers differ only by one bit. The table below illustrates the 3-bit Gray code. 100 111 101 110 111 101 110 100 010 011 011 010 001 001 000 000 Gray Code Binary Code 0 1 2 B B B 0 1 2 G G G a. Find simplified Boolean expressions for the Gray code bits G 0 , G 1 , and G 2 as functions of the input binary bits B 0 , B 1 , and B 2 . (10 points).
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