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sp03-lw-sf

# sp03-lw-sf - ECE 2030 I 6 problems 8 pages Problem 1(3...

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ECE 2030 I Computer Engineering Spring 2003 6 problems, 8 pages Final Exam Solutions 28 April 2003 1 Problem 1 (3 parts, 22 points) Logic Design Consider the following expression: ) ( ) ( ) ( B A C A C B A Out + + = Part A (8 points) Implement the expression using only NOR and NOT gates. Assume you do not have the compliments of the inputs. Use proper mixed logic notation. Do not simplify the expression . Determine the number of transistors used in this implementation. A B C A C A B Out number of transistors: 2 x 6 + 2 x 4 + 5 x 2 = 30T Part B (8 points) Implement the expression using N and P type switches. Assume the inputs, A, B, and C, are available in their true and complemented forms. A B C A C A B A B C A C A B Part C (6 points) Now simplify the expression and produce a sum of products SOP expression. List all prime implicants and indicate which are essential. A A B B C C C prime implicants essential? yes no 1 1 0 0 1 1 0 1 A C A C A B B C simplified SOP expression B A C A C A + + or C B C A C A + +

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ECE 2030 I Computer Engineering Spring 2003 6 problems, 8 pages Final Exam Solutions 28 April 2003 2 Problem 2 (2 parts, 20 points) Counter Design Part A (6 points) Design a toggle cell using only transparent latches, inverters, and 2-to-1 multiplexers. Use icons for the latches and muxes. Your toggle cell should have an active high toggle enable input TE , and an active low clear input Clear , two-phase non-overlapping clock inputs Φ 1 and Φ 2 , and a single output Out . The Clear signal has precedence over TE . Label all signals . In Out En Latch In Out En Latch TE Out Clear Φ 1 Φ 2 MUX Sel 1 0 0 MUX Sel 1 0 Part B (14 points) Now use several of your toggle cells (in icon form) to build a
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