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You are here: Home / Electronics / Digital Logic Circuits / Laws Of Boolean Algebra
Laws Of Boolean Algebra

Laws Of Boolean Algebra

November 17, 2018 by Andrea Fonseka

Laws Of Boolean Algebra

The Laws Of Boolean Algebra is provided here.

OR

A + 0 = A

A + A’ = 1

A + B = B + A

A (B + C) = AB + AC

A + A = A

A + 1 = 1

A + AB = A

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

A” = A

AND 

A . 1 = A

A . A’ = 0

A . B = BA

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

A . A = A

A . 0 = 0

A (A + B) = A ,     ( AA+ AB = A, A + AB = A)

A (BC) = (AB) C

Distributive Law: 

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

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

Associative Law: 

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

A . (B .C) = (A . B) . C

Demorgan’s Theorem: 

1. (AB)’ = A’ + B’

The product of the compliment is equal to the sum of the compliments

Proof:

A B A’ B’ (AB) (AB)’ A’ + B’
0 0 1 1 0 1 1
0 1 1 0 0 1 1
1 0 0 1 0 1 1
1 1 0 0 1 0 0

 

2.(A + B)’ = A’ . B’

The sum of the compliment is equal to the product of the compliments.

Proof: 

A B A’ B’ (A + B) (A + B)’ A’. B’
0 0 1 1 0 1 1
0 1 1 0 1 0 0
1 0 0 1 1 0 0
1 1 0 0 1 0 0

 

 

 

 

 

 

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