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Boolean Arithmetic:
Let us begin our exploration of Boolean algebra by adding numbers together:
0 + 0 = 0
0 + 1 = 1
1 + 0 = 1
1 + 1 = 1
The first three sums make perfect sense to anyone familiar with elementary addition. The
Last sum, though, is quite possibly responsible for more confusion than any other single statement in digital electronics, because it seems to run contrary to the basic principles of mathematics.
Well, it does contradict principles of addition for real numbers, but not for Boolean numbers.
Remember that in the world of Boolean algebra, there are only two possible values for any quantity and for any arithmetic operation: 1 or 0. There is no such thing as ‖2‖ within the scope of
Boolean values. Since the sum ‖1 + 1‖ certainly isn‘t 0, it must be 1 by process of elimination.

Boolean addition corresponds to the logical function of an ‖OR‖ gate,
as well as to parallel switch contaBoolean addition corresponds to the logical function of an ‖OR‖ gate,
as well as to parallel switch contacts:
There is no such thing as subtraction in the realm of Boolean mathematics. Subtraction
Implies the existence of negative numbers: 5 - 3 is the same thing as 5 + (-3), and in Boolean algebra negative quantities are forbidden. There is no such thing as division in Boolean mathematics, either, since division is really nothing more than compounded subtraction, in the same way that multiplication is compounded addition

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