Boolean AND one

If we have an expression like:

A\cdot 1

…then for any value of A, we are ANDing it with one. If we and anything with 1, then we just get back the value A.

We know that, because of the AND truth table:

• 1 AND 1 = 1
• 0 AND 1 = 0, so:
• A AND 1 = A

In short:

A\cdot1=A

We can use this to simplify boolean algebra!