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290 Written HW 1

# 290 Written HW 1 - Mallard ECE 290 Computer Engineering I...

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Mallard ECE 290: Computer Engineering I - Spring 2007 - Written HW... https://mallard.cites.uiuc.edu/ECE290/material.cgi?SessionID=mding3_... 1 of 3 1/21/2007 11:44 PM Written HWK #1 (due 3:00 pm on 1/24/2007) ECE 290 Homework Set #1 Due: January 24, 2007 ©D. J. Brown & C. N. Hadjicostis Problem 1.1 Suppose you have an object which is known to have an integral weight of between 1 gram and 40 grams. You are to use a balance scale (with 2 weighing pans) in order to determine the precise weight of the object. (a) Suppose you are given a set of 8 measuring weights of: 1, 1, 3, 3, 9, 9, 27, 27 grams. Show how you would weigh a 17 gram object. A 31 gram object. i. Explain why this set of weights can weigh any object from 1 to 40 grams. Your explanation should use the concept of base r numbers; do not simply enumerate the cases. ii. (b) In part (a) you used 8 measuring weights, whereas only 4 are needed: specify their sizes. Repeat part (a), (i) and (ii), using these 4 weights. Problem 1.2 In a low-power CMOS (Complementary Metal Oxide Semiconductor) logic circuit that counts (up or down but not both), power is consumed only when a bit changes. In fact, it is commonly assumed (and we will also assume it here) that the power consumed is directly proportionate to the average number of bit flips per count. We are given a counter of n bits that counts from 0 to 2^(n-1). (a) Let n=4. What is the power consumed for continuous upward counting (with wrap-around) at the outputs of a standard binary counter? (You can take the consumed power to be a known constant C times the average number of bit flips per count.) What is the percentage of power consumed for continuous upward counting

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