CODEWITHSUNDEEP
logic
Georgiana M
Georgiana M

Reputation: 431

How to write a logic expression with only NAND gates

I want to convert a logical expression to have only NAND gates. I know that NAND is written as ¬(A⋀B).

I have the following expression: (A⋁(¬B))⋀C

How to write this expression only with NAND?

Upvotes: -1

Views: 739

Answers (1)

Surendra Shrestha
Surendra Shrestha

Reputation: 1080

Y = (A ⋁ (¬B)) ⋀ C
  = ¬¬{(A ⋁ (¬B)) ⋀ C}      //Double negation
  = ¬{¬(A V (¬B) V ¬C}      //De-Morgan law
  = ¬{(¬A ⋀ B) V ¬C}        //Reverse De-Morgan law
  = ¬{(¬A V ¬C) ⋀ (B V ¬C)} //Distributive law
  = ¬{¬(A ⋀ C) ⋀ ¬(¬B ⋀ C)} //Apply reverse De-Morgan law

Upvotes: 3

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