[11] Convert each of the following expressions into sum of products and product of sums : (a) F = (AB+C)(B+CD) (b) F = x + x(x + y) (y + z)
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College of Computers & Information Technology Digital Logic Design 503221-4 |
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Solved in 3 steps
- 1- The function F (x,y,z) = x'y' + yz is equivalent to: a ) Ση(2,3 ,4) b) Σm(2,3 ,5) C) Σm(1,2 ,5) d) Σm( 0,1,3,7)1.Express the following functions in sum of minterms and product of maxterms : (a) F (A,B, C,D) = B'D+ A'D+ BD (b) F (x, y, z) = (xy+ z)(xz+ y)Quèstion 14 This function F=xy + x'z can be expressed as a product of sum as one of the following: O (x +y)(x+Z)(y+z) O (x'+z)(x+y)(y+z) O (x'+y)(x+z)C y+z) O None of the mentioned
- 1- Express the following function as a sum of products and as a product of sums. F(w, x, y, z) = yw+xw+z'w' 2- Convert each of the following to the other canonical form a. F(x,y,z) = {(1,2,6) b. F(w, x, y, z) = (2,4,8,9)2. Generate truth table for the following functions:(a) F(X,Y,Z)=∑(1,3,6,7)(b) F(X,Y,Z)=π(1,3,4)(c) F(W,X,Y,Z)=∑(1,4,7,10,12,15)(d) F(W,X,Y,Z)=π(2,3,4,7,10,11,12,13)Simplify B (x, y, z) = X’Z+X’Y+YZ
- a) Prove the following identity by algebraic manipulation: AB + A' C + BC = AB+A' C b) For the following function, i. Rewrite the following in the Sum of Minterms (SOM) form and in the Product of Maxterms form. ii. Show the truth Table [(x, y, z) = xy'(ztx') +y'(z'tx)Create the Kmaps and then simplify for the following functions: a) F(x.y.z) = x'y'z' + x'yz + x'yz b) F(x,y,z) = x'y'z' +x'yz' + xy'z' + xyz'Q.3 a) Prove the following identity by algebraic manipulation: AB + A'C+ BC = AB + A' C b) For the following function, i. Rewrite the following in the Sum of Minterms (SOM) form and in the Product of Maxterms form. Show the truth Table ii. f(x, y, z) = xy'(z+x') + y'(z'+x)
- Express the following function as a sum of minterms and as a product of max terms: F(A, B,C, D) = B'D + A'D + BDc) Realize the expression F(a,b,c,d)=bc' + a'b'd + bcd' + ab'd product of sum. with a minimum1) Simplify the following Boolean functions, using three variable K-maps. a) F(x, y, z) = Σ(0, 1, 2, 3, 5) b) F(x, y, z) = x'y + yz' + y'z'