Convert the following to the other canonical form: (a) F(x, y, z) = Σ (1, 3, 7)      (b) F(A, B, C, D) =  Π (0, 1,2,3,4,6,12)

1. Simplify the following Boolean functions, using three-variable Kmaps: (a) F(x, y, z) = Σ(0, 1, 5, 7) (b) F(x, y, z) = Σ(1, 2, 3, 6, 7) (c) F(x, y, z) = Σ(2, 3, 4, 5)

3.3. Using DeMorgan's Law, write an expression for the complement of F if F(x, y, z) = xỹ(x + z).

Compute the following values of ψ(X, B), the number of B-smooth numbers between 2 and X. (c) ψ(50, 7)

SOP FORM DIGITAL( NEED NEAT HANDWRITTEN SOLUTION ONLY OTHERWISE DOWNVOTE).

PaoBLEM# 3:33 1 Simplify the following Boolean function F(), together with the don't-care conditions d. Express the simplified function in sum of minterms. . F (X, Y,Z) Σm (0 , 1, 2, 4, 5) + Σ d (3, 6, 7) • F(A,B,C, D) = Em(1,3,5,7,9,15) +Ed(4,6,12,13)

4. Karnaugh Maps Simplify parts a through d using Karnaugh maps a) F(x.y.)-Σ(0,2,4,5) b) F(x,y,z)=x'y'+yz+x'yz' c) F(w,x,y,z)=E(2,3,12,13,14,15) d) x'z+w'xy'+w(x'y+xy') e) Find minterms of xy+yz+xy'z by plotting it in a Karnaugh map. f) Find all the prime implicants of F (w, x, y, z)=E(0, 2, 4, 5, 6, 7, 8, 10, 13, 15) Determine which are essential. g) Simplify F (A, B, C, D)=E(1, 3, 4, 5, 10, 11, 12, 13, 14, 15) using essential prime implicants.