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Unformatted text preview: ECE 3060 Sample Test II
1. Two level minimization a) Suppose we have an A matrix as specified below. Using the branch and bound algorithm, find a selection vector x which represents a minimum cover. 0 1 0 A= 0 1 0 1 1 0 1 0 1 0 0 1 0 0 1 1 0 0 0 1 0 b) Suppose F=w'xy' + wyz + wxy + w'yz. Give an implicant table for F. c) Using the tabular method of QuineMcCluskey, find all prime implicants of F from b). 2. Binary Decision Diagrams a 0 1 b 0 0 d 1
0 1 1 c 1 0 a) What function is represented by this BDD? b) What classification (type) of BDD is this? c) Is a ' b' covered by the function associated with this BDD? d) Is b'c covered by the function associated with this BDD? 3. Consider the function G = abc + be + f . a) Find the kernel set for G. b) Find the cofactors Ga and Ga c) Write an expression for G in terms of the two cofactors found in (b). 4. Technology Mapping Consider a technology library (with load dependent delay costs) containing a NAND2 (cost=2+2l), NOR2 (cost=2+3l) INV (cost=1+l), and OAI21 (cost=3+2l). Input load for each gate is given by NAND2 (1), NOR2(2), INV (1), and OAI21 (2). (a) Using the base function symbols for a NAND2, for inputs, draw the pattern trees for the library. for an inverter, and a hashed circle (b) Using the circuit shown, draw the subject tree using the symbols from part a), and perform the dynamic programming technology mapping algorithm FOR DELAY as presented in class. Use load bins of 1 and 2. Assume that the primary inputs (a,b,c,d) have delay cost of 1+l. You must show each step of the algorithm. A correct answer with no (correct) work will receive no credit.
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This note was uploaded on 07/30/2009 for the course ECE 3060 taught by Professor Shimmel during the Spring '07 term at Georgia Institute of Technology.
 Spring '07
 Shimmel

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