HW1_ by Zamir Chowdhury.pdf

Which one of the following represents the minterms of

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Which one of the following represents the minterms of F; a- F=A`B`C`D`+ AB`CD` + ABC`D+ ABCD b- F=A`B`C`D`+ AB`CD` + ABC`D+ A`BCD c- F=A`B`C`D`+ AB`CD` + AB`C`D+ ABCD d- F=A`B`C`D`+ A`B`CD` + ABC`D+ ABCD e- F=A`B`C`D`+ AB`CD` + AB`C`D+ ABC`D ii- Use the K-map of F to select one of the following simplified sum of products (minterms). AB CD 00 01 11 10 00 01 1 1 11 1 1 1 1 10 1 1 1 1 AB CD 00 01 11 10 00 0 1 4 12 8 01 1 5 13 1 9 11 3 7 15 1 11 10 2 1 6 14 10 E B D C

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a- F=A`BD` + ABD b- F=A`B`D + ABD c- F=A`B`D` + ABD d- F=A`B`D + ABD` e- F=A`B`D + A`BD` iii- Which one is the logic diagram of the simplified F using combinations of multiple inputs; NOT, AND, OR gates. ii- a- b- c- d- e- iii- Using the following Don’t Care function d with F, which one of the following is the simplified function for F+d in sum of product (minterms) d(A, B, C, D) = Σ (1,3,9,11, 8,10,12, 14) K-map a- F=B`+A b- F=A`+B` c- C`+D d- B+C e- B`+C` 6- Which one of the following represents the following sum of products (minterms) of F(X,Y,Z,W)= Σ (1,3,4,11, 7,10,12, 14) AB CD 00 01 11 10 00 0 1 4 12 x 8 x 01 1 x 5 13 1 9 x 11 3 x 7 15 1 11 x 10 2 1 6 14 x 10 x F A B D A B D F A B D A B D F A B D A B D F A B D A B D F A B D A B D C A E
a- F=X`Y`Z`W+XYZ`W+XYZW+X`YZW+ X`Y`Z`W`+X`YZ`W`+XYZW`+X`Y`ZW b- F=X`Y`ZW`+XYZ`W+XYZW+X`YZW+ X`Y`Z`W`+X`YZ`W`+XYZW`+X`Y`ZW c- F=X`Y`ZW`+XYZ`W+XYZW+X`YZW+ XY`Z`W`+X`YZ`W`+XYZW`+X`Y`ZW d- F=X`Y`Z`W+X`Y`ZW+X`YZ`W`+XY`ZW+ X`YZW +XY`ZW`+XYZ`W`+XYZ`W e- F=X`Y`Z`W+X`Y`ZW+X`YZ`W`+XY`ZW+ X`YZW +XY`ZW`+XYZ`W`+XYZW` 7- Which one of the following represents the product of sums (maxterms) of F(X,Y,Z)= Π (1,3,4,2, 7) a- F=(X`+Y`+Z)(X`+Y+Z)(X+Y`+Z`)(X`+Y+Z`)(X+Y+Z) b- F=(X`+Y`+Z)(X`+Y+Z)(X+Y`+Z`)(X`+Y+Z`)(X`+Y`+Z`) c- F=(X+Y+Z`)(X+Y`+Z`)(X`+Y+Z)(X+Y`+Z)(X`+Y`+Z`) d- F=(X`+Y`+Z)(X`+Y+Z)(X+Y`+Z`)(X+Y`+Z)(X`+Y`+Z`) e- F=(X+Y+Z`)(X`+Y+Z)(X+Y`+Z`)(X+Y`+Z)(X`+Y`+Z`) 8- Given the following Boolean function in sum-of-products form (minterms) F(A, B, C, D) = Σ (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) ii- The following four-variable K-map is used to simplify F(A,B,C,D) in sum of products.

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• Spring '10
• DR.WEEKS
• Boolean Algebra, +ABC, Y c

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