(a) F(X, Y, Z) = YZ + (X+ Y) +(XYZY (b) F(X, Y, Z) = (X+Y+ Z)' (X + Y) %3D %3D
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- 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)Q1) Simplify the following Boolean functions using Karnaugh map method: A. F (D,C,B,A) =£ m(0,1,2,3,4,5,7,11,15) d (6,8,10). B. F (D,C,B,A)= E m(1,3,9,11,12,14,) d (6,7,8,10, 13).Given the following function: f(x) = 2x For g(x) = Sf(x) dx, determine g(x).
- Let f(A, B) = A B, simplified expression for function fi f(x+ y, y), z) is2) Simplify the following Boolean functions, using K-maps. F(x, y, z) = xy + xy' z' + x'y z'Show that the function F(x,y,z) = xy + xz + yz will have a value of 1 if there are at least 2 variables x,y and z which have a value of 1. (using a table)
- Given the following functions: f(x) g(x) = x + 4 = x + 10x + 24 Find each of the values below. G a. (f + g)( – 1) = b. (f – 9)( – 3) = с. (f 9)(— 2) - ()(- 5) = d.Create K-maps and then simplify for the following functions. 3) F(x, y, z) = xyz + xy’z’ + x’yz + x’y’z5. Simplify the following functions using a K-map:(a) F(X,Y)¼m2+ m3
- 5. Simplify the following Boolean functions f, together with the DON'T CARE conditions D, and then express the simplified function in sum of minterms. b) F(A,B,C,D) = E(0, 4, 8, 12, 14) D(4,B,C,D) = D(2, 6, 10) a) F(x,y,z) = E(1, 3, 4, 6) D(x,y,z) = E(0, 2. 5,7) c) F(A,B,C,D)= E(3, 5, 8, 12, 13, 15) D(A,B,C,D) = E(1, 9, 11, 14) d) F(A,B,C,D) = E(1, 3, 6, 9, 15) D(A,B,C,D) = E(0, 2, 10) %3D1) 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'5. For each of the following functions over the positive integers, represented inunary, give the transition diagram of a TM that computes the function. (a). f(x) = ((x+1) mod 2) + 1 (b). g(x) — За +4