simplify the following equation using boolean laws and rules:
x=~(A(+)B) + ~(AB)+~((A(+)B)AC)+(~A)C
(+) means plus in the circle
~ means not
I get ~(ABC)
hey oobleck, thanks but how did you get ~(ABC)
To simplify the given equation using Boolean laws and rules, we can follow these steps:
Step 1: Distribute the negation (~) across the parentheses.
- ~(A(+)B) = ~A * ~B
- ~(AB) = ~A + ~B
- ~((A(+)B)AC) = ~A + ~B + ~A * ~C
The simplified equation becomes:
x = ~A * ~B + ~A + ~B + ~A * ~C + ~A * C
Step 2: Group the common terms.
- x = ~A * (~B + 1 + ~C) + ~B
- x = ~A * (1) + ~B
- x = ~A + ~B
Therefore, the simplified equation is x = ~A + ~B.