homework2b - (a) F ( W,X,Y,Z ) = Σ m (1 , 2 , 3 , 5 , 7 ,...

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CS223 - FALL 2009 Homework #2b Due Friday October 12, 2009 by 16:00 in the Computer Eng. Dept. office (put into CS223 box) [Remember to put your name (and your partner’s name if you choose to work with a homework partner), along with your student ID (s) and section number(s), in the upper right hand corner of each page] 1- Given F ( A,B,C,D ) = ( AB + C )( B + CD ) (a) Find minterms of F and express F in sum of minterms form (b) Find maxterms of F and express F in product of maxterms form 2- Optimize following Boolean functions by means of a map (a) F ( X,Y,Z ) = Σ m (0 , 2 , 4 , 5) (b) F ( A,B,C ) = Σ m (1 , 2 , 3 , 6) 3- Given the function F ( X,Y,Z ) = X Y + X Z + X. Y . Z Find minterms and maxterms of F. 4- Optimize the following functions using a map (a) F ( A,B,C,D ) = Σ m (1 , 3 , 7 , 8 , 11 , 12 , 15) (b) F ( W,X,Y,Z ) = Σ m (0 , 2 , 3 , 4 , 5 , 6 , 7 , 9 , 11 , 12) 5- Optimize the following functions by finding prime implicants and essential prime implicants
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Unformatted text preview: (a) F ( W,X,Y,Z ) = Σ m (1 , 2 , 3 , 5 , 7 , 8 , 9 , 11 , 12 , 14) (b) F ( A,B,C,D ) = Σ m (0 , 1 , 3 , 7 , 8 , 10 , 11 , 13 , 15) 6- Optimize the following functions togather with don’t-care conditions d. (a) F ( W,X,Y,Z ) = Σ m (0 , 2 , 4 , 5 , 8 , 10) d ( W,X,Y,Z ) = Σ m (6 , 12 , 14) (b) F ( A,B,C,D ) = Σ m (0 , 1 , 3 , 7 , 11 , 13 , 15) d ( A,B,C,D ) = Σ m (8 , 10 , 12 , 14) 1 2 CS223 - FALL 2009 7- Realize the optimized functions in question 5 using two level gate circuits: (a) AND-OR gates and inverters (b) NAND gates only (c) NOR gates only 8-Given the function F ( X,Y,Z ) = Σ m (0 , 3 , 5 , 6) with don’t-care condition d ( X,Y,Z ) = Σ m (2 , 7). Optimize and realize the function using: (a) NAND gates only (b) XOR and XNOR gates only...
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This note was uploaded on 12/27/2009 for the course CS 223 taught by Professor Mehmetbaray during the Fall '09 term at Bilkent University.

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homework2b - (a) F ( W,X,Y,Z ) = Σ m (1 , 2 , 3 , 5 , 7 ,...

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