The basis of this is addition; if we can add two binary numbers, we can just as easily subtract them, or get a little fancier and perform multiplication and division.

Unlike decimal addition, there is little to memorize in the way of rules for the addition of binary bits:

CS 110 Binary Addtion Examples ; CS 110 Binary Subtraction Examples ; Eight-Bit Binary Addition Examples...

The binary addition algorithm operates on two bit patterns and results in a bit pattern.

An important example of this is the Binary Addition Algorithm, where two bit patterns representing two integers are manipulated to create a third pattern which represents the sum of the integers.

Let us consider first the problem of doing addition in decimal. Firstly we need to develop the decimal addition table:

The basic rules of binary addition, subtraction, multiplication, and division and a little bit of information about the binary number system. ... Rules of Binary Addition

The rules for binary addition are: ... In order to perform addition on binary numbers, the carry bits must also be included in the sum. The truth table for full binary addition of the bits in position j is:

Result...

The basis of this is addition; if we can add two binary numbers, we can just as easily subtract them, or get a little fancier and perform multiplication and division. ... Binary Addition Circuit