Boolean AND identity

The identity of any operation is the value that, when we combine it with value x using that operation, we get x back again.

In the case of the AND operation, the identity is 1, because:

• 0 \cdot 1 = 0
• 1 \cdot 1 = 1

This means that if we have a value x and we AND it with 1, we get x back again:

• 0 \cdot 1 = 0
• 1 \cdot 1 = 1

A \cdot 1 = A

Boolean simplification

Knowing this identity can help us simplify expressions. Whenever we see something ANDed with 1, we can just remove the 1 and keep the other value.

For example, if we have the expression A \cdot 1, we can simplify it to just A.