270_W07_FinalExam - The University of Michigan EECS 270:...

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1 The University of Michigan EECS 270: Introduction to Logic Design Winter 2007 Final Exam Professor John P. Hayes Professor Kang. G. Shin Friday April 20, 2007 7:00 to 9:00 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: _______ /20 2: _______ /20 3: _______ /20 4: _______ /20 5: _______ /25 6: _______ /20 7: _______ /20 8: _______ /20 9: _______ /20 10: _______ /30 Total : __ _ /215 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 ten problems with the point distribution indicated on the right. Please keep this in mind as you work
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2 Problem 1 : [Boolean Algebra: 20 points] (a) [6 points] Consider the following CMOS circuit. Write down a Boolean expression for the output F in SOP form. Simplify this expression to as few terms as possible. (b) [14 points] Determine if the following pairs of expressions are equivalent. Answer Yes if they are equivalent, and No if the are not equivalent. ( Here denotes XOR) i) a + (a’b) = a + b Yes_____ No _____ ii) ab + c(a + b) = ab + c(a b) _______ iii) a’b’c + ab’c + abc’ + abc = ab + b’c’ _______ iv) (a + b)’a = a + b’ _______ v) (a’ b) = (a’ + b)(a + b’) _______ vi) (a + b’)(b + c’) = (a + b’)(b + c’)(a’ + c) _______ vii) (abc + a’b)’ = b’ + ac’ _______ Ans. (a): _______________________________________
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3 Problem 2 : [ Binary Numbers: 20 points] Consider an 8-bit two’s-complement integer X = x 7 x 6 x 5 x 4 x 3 x 2 x 1 x 0 . We will modify the notation slightly to allow X to denote certain sets of two’s-complement integers using the following convention. If one of the 8 bits x i in X is always 0, we replace x i by 0; if x i is always 1, we replace x i by 1. For example, if we want to denote the set of even numbers, we can write X = x 7 x 6 x 5 x 4 x 3 x 2 x 1 0. (a) [8 points] Write down a correct expression for X using the above x i /x i ’ notation such that X satisfies each of the following requirements. i)
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270_W07_FinalExam - The University of Michigan EECS 270:...

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