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Computer Architecture HW Assignment1 Result.pdf

# None of the above 8 given the following boolean

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None of the above 8- Given the following Boolean function in sum-of-products form (minterms) F(A, B, C, D) = (1,3,4,5,8,9,10,11,12,13) i- F(A,B,C,D) can be converted into maxterms using the complement. Which one of the following represents the correct product of sums (maxterms) of F(A,B,C,D); a- Π(0,2,6,7,8,14,15) b- Π(0,2,6,7,11,14,15) c- Π(0,3,6,7,14,15) d- Π(0,3,4,7,14,15) e- Π(0,2,6,7,14,15) f- None of the above ii- The following four-variable K-map is used to simplify F(A,B,C,D) in sum of products. Select the correct simplification from the following; a- F(A, B, C, D)= A`B+C`B+B`D b- F(A, B, C, D)= AB`+C`B+B`D c- F(A, B, C, D)= AD+C`B+B`D d- F(A, B, C, D)= A`B+AB`+B`D e- F(A, B, C, D)= AB`+CB+B`D f- None of the above iii- Convert your selection in (ii) using De Morgan’s formula to product of sums and select the one that matches it from the following; a- F(A,B,C,D)= [(A+B`)(C+B`)(B+D`)] b- F(A,B,C,D)= [(A`+B)(C+B`)(B+D`)] c- F(A,B,C,D)=[(A`+D`)(C+B`)(B+D`)] d- F(A,B,C,D)=[(A+B`)(A`+B)(B+D`)] e- F(A,B,C,D)=[(A`+B)(C`+B`)(B+D`)] f- None of the above = = = AB CD 00 01 11 10 00 0 0 4 1 12 1 8 1 01 1 1 5 1 13 1 9 1 11 3 1 7 0 15 0 11 1 10 2 0 6 0 14 0 10 1 = =

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iv- Draw the logic diagram with NAND gates only for the simplified output that you have selected in (iii) and match it to one of the following; a- F(A,B,C,D)= [(A`B)`(C`B)`(B`D)`]`` b- b- F(A,B,C,D)=[(AB`)`(C`B)`(B`D)`]`` c- F(A,B,C,D)=[(AD)`(C`B)`(B`D)`]`` d- F(A,B,C,D)=[(A`B)`(AB`)`(B`D)`]`` = B C B A D A` B C` B A D B ` A B D B` F F F B C A B D B` F
e- F(A,B,C,D)=[(AB`)`(CB)`(B`D)`]`` f- None of the above 9- Use 4 four variable K-map to map a six variable function: f(x,y,z,u,v,w) = m (0,5,7,13,15,16,21,23,29,31,32,36, 40, 44,48,52,56,60 ) The function can be simplified by combining all four maps using Boolean algebra. (0-15,16-31,32-47,48-63). All maps use zuvw variables with xy being used as titles (00,01,10 and 11) for each map. The following is the representations of the four maps; Combine f1+f2+f3+f4 using Boolean algebra and match it to one of the following: a- v`w`(z`u` +x)+y`uw b- v`w`(z`u` +y)+x`uw c- v`w`(z`u` +y)+y`uw d- v`w`(x`u` +y)+y`uw e- v`w`(z`u` +x)+x`uw f- None of the above = B C` B A D A` F x`y`=00 map 1 1 1 1 1 0 5 7 15 13 32 48 1 1 58 12 4 8 1 9 3 11 2 6 14 10 1 1 1 1 1 16 21 23 31 29 28 20 24 17 25 19 27 18 22 30 26 36 44 37 40 33 45 41 35 39 47 43 34 38 46 42 52 60 56 49 53 61 57 51 55 63 59 50 54 62 1 1 1 1 1 1 x`y`uw x`yuw xy`=10 map xy=11 map xy`v`w` xyv`w` x`y=01 map
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• Spring '10
• DR.WEEKS
• Boolean Algebra, +ABC

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