Question

N
20. Evaluate the following for a = 4 and b
(a) a'+b: - ab
(b) a b + ab
a-b
(c) tab
a + b
(d) (a+b)-(a - b)​

Answer 1

Answer:

BOOLEAN THEOREMS:

Boolean algebra helps to analyze a logic circuit and express its operation mathematically. We have several Boolean Theorems that helps us to simplify logic expressions and logic circuits.

Single Variable Theorems:

AND Operation OR Operation

A . 0 = 0 A + 0 = A

A . 1 = A A + 1 = 1

A . A = A A + A = A

A . A’ = 0 A + A’ = 1

Multivariable Theorems:

The multivariable theorems involves more than one variable.

Commutative laws:

A + B = B + A

A . B = B . A

Associative laws:

A + (B + C) = (A + B) + C = A + B + C

A (BC) = (AB) C = ABC

Distributive laws:

A (B + C) = AB + AC

A + BC = (A+B) (A+C)

(A + B) (C + D) = AC + AD + BC + BD

Absorption laws:

A + AB = A

A (A + B) = A

Redundant Literal Rule:

A + A’B = A + B

A’ + AB = A’ + B

A(A’ + B) = AB

Demorgan’s Theorem:

(A+B)’ = A’ . B’

(AB)’ = A’ + B’

This law can be extended to any number of variables or combinations of variables.

How to apply Demorgan’s theorem to an expression?

Complement the entire given expression.

Change all the AND’s to OR’s and all the OR’s to AND’s.

Complement each of the individual variables.

Change all 0s to 1s and all 1s to 0s...

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