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270-W08-Exam1Solns-V21

# 270-W08-Exam1Solns-V21 - The University of Michigan EECS...

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1 The University of Michigan EECS 270: Introduction to Logic Design Winter 2008 Exam 1 Solutions Professor John P. Hayes Professor Kang. G. Shin Wednesday February 6, 2008 8:00 to 9:30 pm Name: ________________________________ UMID: ________________________________ Honor Pledge: “I have neither given nor received aid on this exam, nor have I concealed any violations of the Honor Code.” Signature: ____________________________ 1: _______ /12 2: _______ /16 3: _______ /14 4: _______ /10 5: _______ /12 6: _______ /14 7: _______ /10 8: _______ /12 Total : ______ /100 Instructions The exam is closed book . No books, notes or the like may be used. No computers, calculators, PDAs, cell phones or other electronic devices may be used Print your name, give your UMID, and sign the Honor Pledge above when you are done. Show all your work . You get partial credit for partial answers. The exam consists of eight problems with the point distribution indicated on the right. Please keep this in mind as you work

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2 Problem 1 : [Numbers: 12 points] (a) [2 points] Convert the binary number 11010101 to decimal. 11010101 2 = 128 + 64 + 16 + 4 + 1 = 213 Ans. (a) ___ 213 10 ____________________________________________________ (b) [4 points] Convert the decimal number 67.7 to binary using the divide-by-2 and multiply-by-2 methods. 2) 67 . 7 x 2 2) 33 1 1. 4 x 2 2) 16 1 0. 8 x 2 2) 8 0 1. 6 x 2 2) 4 0 1. 2 x 2 2) 2 0 0. 4 x 2 Repeats from here on 2) 1 0 2) 0 1 Ans. (b) __ 1000011.10110 ___________________________ (c) [4 points] Convert the octal (base eight) number 734 to base five. Step 1: 734 8 = 7 x 64 + 3 x 8 + 4 x 1 = 448 + 24 + 4 = 476 10 Step 2: Using divide-by-5 method 5) 476 5) 95 1 5) 19 0 5) 3 4 5) 0 3 Ans. (c) _____ 3401 5 ____________________________________ (d) [2 points] What is the period (in nanoseconds) of a 2.8 Ghz clock? In general, clock period = 1/frequency where the units used have to be consistent, e.g. seconds (s) and cycles-per-second (hertz). Note that 1 s = 1 x 10 9 ns, and 1 Ghz = 1 x 10 9 cycles/s. Ans. (d) __ 1/(2.8) = 0.3571... ______________________________________
3 Problem 2 : [Gates and basic circuits: 16 points] (a) [4 points] Draw the truth table for a 3-input XNOR (exclusive-NOR) gate that has inputs a,b,c and output z . a b c z 0 0 0 1 0 0 1 0 0 1 0 0 0 1 1 1 1 0 0 0 1 0 1 1 1 1 0 1 1 1 1 0 In general, an n -input XNOR gate outputs a 1 if and only if the number of 1’s applied to the inputs is even.

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270-W08-Exam1Solns-V21 - The University of Michigan EECS...

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