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**3.3 Simplify the following Boolean expression using three-variable maps:**

d) F(x, y, z) = x y z + x\ y\ z + x y\ z\ y yz 00 01 11 10 1 x x z x y z x y\ z \ x\ y\ z

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3.5 Simplify the following Boolean expression using four-variable maps: a) F(w,x, y, z) = (1,4,5,6,12,14,15) y yz 00 01 11 10 1 wx w\ y\ z w x y x z\ x w z F =w\ y\ z+w x y+ x z\

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3.5 Simplify the following Boolean expression using four-variable maps: b) F(A,B,C,D)= (1,5,9,10,11,14,15) C CD 00 01 11 10 1 A\ C\ D AB A C A B\ D B B\ C\ D A D F =A\C\D+AC+(AB\D or B\C\D)

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3.5 Simplify the following Boolean expression using four-variable maps: c) F(w,x, y, z) = (0,1,4,5,6,7,8,9) y yz 00 01 11 10 1 x\ y\ wx w\ x x w z F =x\y\+w\x

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3.5 Simplify the following Boolean expression using four-variable maps: d) F(A,B,C,D)= (0,2,4,5,6,7,8,10,13,15) C CD 00 01 11 10 1 B\ D\ AB B D A\ B B A\ D\ A D F =B\D\+BD+(A\B or A\D\)

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3.6 Simplify the following Boolean expression using four-variable maps: a)A\B\C\D\+AC\D\+B\CD\+A\BCD+BC\D C CD 00 01 11 10 1 B\ D\ AB A\ B D A B C\ B A D F =B\D\+A\BD+ABC\

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**3.6 Simplify the following Boolean expression using four-variable maps: b) x\z+w\xy\+w(x\y+xy\)**

= x\z+w\xy\+wx\y+wxy\ y yz 00 01 11 10 1 x\ z wx x y\ w x\ y x w z F =x\ z+xy\+wx\y

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3.6 Simplify the following Boolean expression using four-variable maps: c)A\B\C\D\+A\CD\+AB\D\+ABCD+A\BD C CD 00 01 11 10 1 B\ D\ AB A\ B D B C D B A\ B C A\ C D\ A D F =B\D\+A\BD+BCD+(A\BC or A\CD\)

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3.6 Simplify the following Boolean expression using four-variable maps: d)A\B\C\D\+AB\C+B\CD\+ABCD\+BC\D C CD 00 01 11 10 1 A\ B\ D\ AB B C\ D A C D\ B A B\ C A D F =A\B\D\+BC\D+ACD\+AB\C

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3.10 Simplify the following Boolean function by first finding the essential prime implicants:c) F(A,B,C,D)=(1,3,4,5,10,11,12,13,14,15) C CD 00 01 11 10 1 B C\ essential AB A C essential A\ B\ D essential B A B non-essential A A\ C\ D non-essential B\ C D non-essential Redundant D F =BC\+AC+A\B\D

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3.13 Simplify the following Boolean expression to (1) sum-of-products (2) product-of-sums b) ACD\+C\D+AB\+ABCD 1) C CD 00 01 11 10 1 C\ D AB A C A B\ B A D F = C\D+AC+AB\

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3.13 Simplify the following Boolean expression to (1) sum-of-products (2) product-of-sums b) ACD\+C\D+AB\+ABCD 2) C CD 00 01 11 10 1 A\ D\ AB A\ C B C\ D\ B A F\ = A\D\+A\C+BC\D\ D F = (A+D)(A+C\)(B\+C+D)

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