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hw8 - Assume that we can implement AND and OR gates with an...

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ECEN 248: Introduction to Digital System Design Department of Electrical Engineering Texas A&M University Assignment #8 Due Thursday,November 19, 2009 1. [20 points.] Consider a function f = ab + b c . (a) Write down the recursive Shannon expansion of this function, by using the cofactoring order a b c . (b) Using this as a starting point, implement f with the minimum number of MUXes. (c) Suppose the cofactoring order is changed to b a c . Re-do the recursive Shannon expan- sion, and from this, find the new implementation of f with the minimum number of MUXes. 2. [15 points.] Suppose I have an n -input XOR function. I want to implement it in two different ways, and compare the cost of these implementations. (a) Suppose I implemented it using AND, OR and INVERTER gates. How many gates do I need?
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Unformatted text preview: Assume that we can implement AND and OR gates with an arbitrary number of inputs. (b) Now suppose I implement this function using MUXes and INVERTERs. How many MUXes or INVERTERs do I need? 3. [15 points.] In this question, we will practice representing a number in different bases or formats. (a) Express-13 . 239 × 2-47 in IEEE single precision floating point format (b) Express 39 . 1955 × 2 147 in IEEE double precision floating point format. (c) Convert 24458 9 to base 7. (d) Suppose A is the largest number that I can represent using IEEE double precision floating point. Also suppose B is the largest number I can represent using 64-bit unsigned arithmetic. What is the ratio A/B ? 1...
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