Question

Simplify F(A, B, C) = A.B + A.B' + B.C' using Boolean

theorems​

Answer 1

Answer:

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Explanation:

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.