Laws Of Boolean Algebra

Excess-3 to BCD logic diagram

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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