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Duality and Complementary

Before see the examples please follow previous chapter:  Laws of Boolean Algebra

Duality or Dual Expression: 

Duality theorem used to convert positive logic to negative logic and vice versa.

Positive Logic Negative Logic

Logic 0 – 0V                             Logic 0 – +5V

Logic 1 – 5V                             Logic 1 – 0V

How dual an expression:

1. Change AND by OR and OR replace by AND.  (AND ↔ OR)

2. 1 replace by 0 and vice versa.  (1 ↔ 0)                 

3.  Keep all literals as same.

Example:

Dual of above expression:

Note: There is no change in complement.

Some more examples:

Dual of above Expression:

We can rewrite this above Boolean expression as

(See Transposition Law at chapter:  Laws of Boolean Algebra)

Dual of above Expression:

Complementary:

How complementary an expression:

1. Change AND by OR and OR replace by AND.  (AND ↔ OR)

2. 1 replace by 0 and vice versa.  (1 ↔ 0)                 

3. Complement all literals to uncomplement and vice-versa. 

Example: