270_W07_FinalExam

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

This preview shows pages 1–4. Sign up to view the full content.

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

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
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): _______________________________________
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)

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 13

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

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online