hw12Sol - CSE 260 Digital Computers Organization and...

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Unformatted text preview: CSE 260 Digital Computers: Organization and Logical Design Homework 12 Solutions Jon Turner April 17, 2008 1. (4 points) Find complements for the following expressions. (a) (A + B + C D)(B + D ) AB(C+D) + BD (B+D )((A + D)C + BD ) (b) B D + (A D + C)(B + D) 2. (4 points) For each expression, list all of its minterms and maxterms. (a) (A + C)B the minterms are A BC , A BC, ABC (or 2,3,7) the maxterms are numbered (0,1,4,5,6) and are (A+B+C), (A+B+C ), (A +B+C), (A +B+C ), (A +B +C) (b) AC + A(C + B D) the SOP form is AC + AC + AB D, so the minterms are A B C D , A B C D, A BC D , A BC D, AB CD , A B CD, A BCD , A BC D, A BCD (or 1,2,3,6,7,8,9,12,13) the maxterms are numbered (0,4,5,10,11,14,15) and are (A+B+C+D), (A+B +C+D), (A+B +C+D ), (A +B+C +D), (A +B+C +D ), (A +B +C +D), (A +B +C +D ) -1- 3. (10 points) For each function given below, find the minimal sum-of-products form, and the minimal product of sums form using a Karnaugh map. (a) F(A,B,C) = m(0,1,2,4,5) (b) F(A,B,C,D) = m(0,2,3,4,6,7,8,9,14,15) 00 01 11 10 BC 00 01 11 10 BC A 0 1 1 1 0 1 1 1 0 0 A 0 1 1 1 0 1 1 1 0 0 (a) F(A,B,C) = m(0,1,2,4,5) = AC + B F (A,B,C) = AB+BC F(A,B,C)= (A+B)(B+C) CD 00 00 01 11 10 00 00 CD 01 11 10 1 1 0 1 0 0 0 1 1 1 1 0 1 1 1 0 AB 1 1 0 1 0 0 0 1 1 1 1 0 1 1 1 0 AB 01 11 10 01 11 10 (b) F(A,B,C,D) = m(0,2,3,4,6,7,8,9,14,15 ) = ABC + BC +AC+AD F (A,B,C) = ABC+ACD+ABC F(A,B,C)= (A+B+C)(+C+D)(A+B+C) -2- 4. (6 points) For each function given below, simplify it using a 4 variable Karnaugh map, taking advantage of the don't care conditions. (a) F(A,B,C,D) = m(0,4,14,15), d(A,B,C,D) = m(3,6,7,11,12) (b) F(A,B,C,D) = m(2,7,8,12,15), d(A,B,C,D) = m(3,6,9,14) (a) F(A,B,C,D) = m(0,4,14,15), d(A,B,C,D) = m(3,6,7,11,12) = ACD + BC CD 00 00 01 11 10 1 1 x 0 0 0 0 0 x x 1 0 0 x 1 x AB 00 01 11 10 CD 00 01 11 10 AB 01 11 10 0 0 1 1 0 0 0 x x 1 1 0 1 x x 0 (b) F(A,B,C,D) = m(2,7,8,12,15), d(A,B,C,D) = m(3,6,9,14) = AC + BC + CD -3- ...
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This note was uploaded on 11/12/2010 for the course KTMT KTMT04 taught by Professor Son during the Spring '10 term at Dallas Colleges.

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