2. (a) Compute and simplify f = (xz+ (y+t)' + (xz)'y')' Encircle final answer! (b) Prove or disprove that in any Boolean algebra, B: (i) 0' = 1
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- Boolean Algebra Simplify the following functions to a minimum number of literals. Show step-by-step simplification and indicate the theorem/postulate used in each step. Draw the logic diagram of each of the simplified functions. (x’y’ + z)’ + z + xy + wz4. Simplify the following Boolean function F, together with the don’t-care conditions d, and then express the simplified function in sum-of-minterms form: a. F(x,y,z) = Σ(0,1,4,5,6) d(x,y,z) = Σ(2,3,7) b. F(A,B,C,D) = Σ(0,6,8,13,14) d(A,B,C,D) = Σ(2,4,10)solve problem D Given the Boolean function: F = xy' + z'y'z + xyz d) List the truth table or the functlon from the simplified expression and show that it is the same as the truth table in part (a).
- Simplify the following Boolean function F, together with don’t care conditions d and then express the simplified function in sum-of-minterms form. (a) F (x,y,z) = ∑ (0,1,4,5,6) d (x,y,z) = ∑ (,2,3,7)9. Show that De Morgan's Law applies to Boolean algebra, by showing that for all x and y, (x ⋁ y)’ =x’ ⋀ y’ dan (x ⋀ y)’ = x’ ⋁ y’Demonstrate the validity of the following identities by means of truth tables: The distributive law: x + yz = ( x + y ) ( x + z )
- Boolean Algebra Simplify the following functions to a minimum number of literals. Show step-by-step simplification and indicate the theorem/postulate used in each step. Draw the logic diagram of each of the simplified functions. (A’ + C)(A’ + C’)(A + B + C’D)Answer the given question with a proper explanation and step-by-step solution. Which of the following minterm expansion forms represents the Boolean function f(x,y):f(0,0)=0, f(0,1)=0,f(1,0)=1,f(1,1)=1 ?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)
- Simplify the following Boolean function F, together with the don’t-care conditions d, and then express the simplified function in sum-of-minterms form: F (x, y, z)=Σ(0, 1, 4, 5, 6) d(x, y, z)=Σ(2, 3, 7)6: Prove the identity of each of the following Boolean equations, usingalgebraic manipulation:(a) XY + XY + XY = X + Y(b) AB + BC + AB + BC = 1(c) Y + XZ + XY = X + Y + Z(d) XY + YZ + XZ + XY + YZ = XY + XZ + YZDemonstrate the validity of the following identities by means of truth tables: DeMorgan’s theorem for three variables: ( x + y + z ) ′ = x ′ y ′ z′ and ( xyz ) ′ = x ′ + y ′ + z ′