CODEWITHSUNDEEP
booleanboolean-logicboolean-expression
potatomeister
potatomeister

Reputation: 65

Simplifying boolean expressions help (tried rules but confused)

ABD+ABC+ABCD

I understand that AB is the common factor so I think it becomes:

AB(D+C+CD)
AB(D(1+c)+C)
AB(C+D)

or

AB(D+C+CD)

use commutative law? (i think thats what its called) AB(CD+D+C) AB(C+D)

Please help, I'm very confused with this

Upvotes: 1

Views: 58

Answers (1)

Yash Bansal
Yash Bansal

Reputation: 118

this is the last step. AB(CD+D+C) => AB(C+D(1+C)) => AB(C+D)

A(1+B)== A(true) .1+B IS always true. this could be thought as (true or expression) which is always true.

Think of the truth table of OR operator.

A B value

0 0 0

0 1 1

1 0 1

1 1 1

here we have value =1 for all the cases where one of the exp =1. Thats all you need.

Commutative law states that A+B=B+A.

This is because truth table of A+B is same as B+A.

Upvotes: 1

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