Find the complement of Y(a,b)=ab’+a’b, and prove that Y+Y'=1. Give a reason for each step.

Question

Question

Find the complement of Y(a,b)=ab’+a’b, and prove that Y+Y'=1. Give a reason for each step.

engineering Computer-Science

Answer 1

Answer #1

--> Y(a,b) = ab’+a’b

--> complementing Y gives

Y'(a,b) = (ab’+a’b)'

= (ab')' . (a'b)' (DeMorgan's law)

= (a' + b).(a+b') (DeMorgan's law)

= a'(a+b') + b(a+b') (Distributive law)

= a'a + a'b' + ab + bb' (Distributive law)

= ab + a'b' (Complement law)

--> Y' = ab + a'b'

--> Y + Y' = ab’+a’b + ab + a'b'

= a(b+b') + a'(b+b')

= a.1 + a'.1 (Complement law)

= a+a' (Identity law)

= 1 (Complement law)

Answer 2

Similar Homework Help Questions

3. a) Simplify the expression (ab + a’b’)(cd + c’d’) + (ab)’ b). Prove that the...

3. a) Simplify the expression (ab + a’b’)(cd + c’d’) + (ab)’ b). Prove that the expression x’y XOR xy’ = x XOR y is true. c). Simplify the function f(x, y, z) = xyz’ + xy’z’ + x’y as much as possible and give the CPOS and CSOP of f
Prove with Boolean algebra that (x - y) + (x'-y)-y. Give a reason for each step...

Prove with Boolean algebra that (x - y) + (x'-y)-y. Give a reason for each step in your proof.
12. Prove the following properties of Boolean algebras. Give a reason for each step. a. (x...

12. Prove the following properties of Boolean algebras. Give a reason for each step. a. (x + y x) b. x.(z+y) + (x' + y)' = x

Given: F(A,B,C) = A’B + AB’ and G(A,B,C) = A’BC’ + AB’C’ + A’BC...

Given: F(A,B,C) = A’B + AB’ and G(A,B,C) = A’BC’ + AB’C’ + A’BC + AB’C Prove that F(A,B,C) = G(A,B,C)
Simplify Y = AB’ + (A’ + B)C. a) AB’ + C b) AB + AC...

Simplify Y = AB’ + (A’ + B)C. a) AB’ + C b) AB + AC c) A’B + AC’ d) AB + A
1) Implement each side with gates, that is a block diagram/schematic a+(b+c) = (a+b)+c a(b+c) =...

1) Implement each side with gates, that is a block diagram/schematic a+(b+c) = (a+b)+c a(b+c) = ab + ac 2) Make a truth table for each of the functions below and identify where each term comes from in the truth table a. F=X’Y+Y’Z’+XYZ b. G=XY+(X’+Z)(Y+Z’) c. H=WX+XY’+WX’Z+XYZ’+W’XY’ 3) For the expression F = A’B’C + ABC + ABC’ How many literals are there ___________ How many terms are there ___________ 4) F(a,b,c,d) = m(0,1,4,7,12) Find the canonical sum (which is...

Find the complement of the following expressions b) (AB+C)0%E 2. Given the Boolean function F -xy...

Find the complement of the following expressions b) (AB+C)0%E 2. Given the Boolean function F -xy + x'y' y'z 1. Implement it with AND, OR, and inverter 2. Implement it with OR and inverter gates, and 3. Implement it with AND and inverter gate 3. Express the following function in sum of minterms and product of maxterms: a) F(A,B,C,D) - B'DA'D BD b) F (AB+C)(B+C'D) 4.Express the complement of the following function in sum of minterms a) F (A,B,C,D)-2 (0,2,6,11,13,14)...
Draw the nonabbreviated logic diagram for Boolean expression (a'+b')((b'+c)+b'c) and prove it equals to b'+a'c. Give...

Draw the nonabbreviated logic diagram for Boolean expression (a'+b')((b'+c)+b'c) and prove it equals to b'+a'c. Give a reason for each step in your proof.
please give explanation and step by step solution! 3. (a) Prove that if [an converges, then...

please give explanation and step by step solution! 3. (a) Prove that if [an converges, then for all r EN, lim (an + ... + an+r) = 0. n+00 (b) Is the converse true? Prove or find a counterexample.

1. (a) Prove by algebraic method that ¯a + ab + ac¯+ a ¯bc¯ = ¯a...

1. (a) Prove by algebraic method that ¯a + ab + ac¯+ a ¯bc¯ = ¯a + ¯b + ¯c. (b) Find the CPOS of f(x, y, z) = (x + ¯y)y + ¯xz + x + y + ¯y(x + z).