CODEWITHSUNDEEP
booleanboolean-logicboolean-expressionboolean-algebra
Lurkki
Lurkki

Reputation: 1

Is this boolean conversion correct?

I have a boolean expression that looks like this

(!B and !C) or (B and !D) or (A and !C)

And I need to convert it so that it only has and operations. So I came up with this result

(B and C) and (!B and D) and (!A and C)

Is this correct or am I doing something wrong? I just want to make it sure.

I also know that

A or B

Is equilevant to

!(!A and !B)

Upvotes: 0

Views: 31

Answers (2)

Kevin
Kevin

Reputation: 100

The two expressions are not equivalent. The second one is the dual of the first one. The expression is already in the minimal Sum-of-Product form.

Upvotes: 0

Axel Kemper
Axel Kemper

Reputation: 11322

If you apply your last expression to replace OR by AND, you can rewrite your Boolean expression to

!(!(!B and !C) and !(B and !D) and !(A and !C))

But the Boolean expression can be simplified to

!C or (B and !D)

Karnaugh map:

         cd
       00  01  11  10
      +---+---+---+---+
   00 | 1 | 1 | 0 | 0 |
      +---+---+---+---+
   01 | 1 | 1 | 0 | 1 |
ab    +---+---+---+---+
   11 | 1 | 1 | 0 | 1 |
      +---+---+---+---+
   10 | 1 | 1 | 0 | 0 |
      +---+---+---+---+

This can be expressed as

!(C and !(B and !D))

Upvotes: 0

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