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## Arithmetic Operations

Addition is a form of counting in which one quantity is added to another. The following definitions identify the basic terms of addition:

SUM - The result of an addition (the sum of 5 and 7 is 12)

Let's start by adding two binary bits. Since each bit has only two possible values, 0 or 1, there are only four possible combinations of inputs. These four possibilities, and the resulting sums, are:

0 + 0 = 0

0 + 1 = 1

1 + 0 = 1

1 + 1 = 10

Example 1

Example 2

Example 3

### Subtraction of Binary Numbers

The following definitions identify the basic terms you will need to know to understand subtraction operations:

SUBTRACT - To take away, as a part from the whole or one number from another

MINUEND - The number from which another number is to be subtracted

SUBTRAHEND - The quantity to be subtracted

REMAINDER, or DIFFERENCE - That which is left after subtraction

Now that you are familiar with the addition of binary numbers, subtraction will be easy. The following are the four rules that you must observe when subtracting:

The following example (101102 - 11002) demonstrates the four rules of binary subtraction:

Rule 4 presents a different situation because you cannot subtract 1 from 0. Since you cannot subtract 1 from 0 and have a positive difference, you must borrow the 1 from the next higher order column of the minuend. The borrow may be indicated as shown below:

1 from the next higher order column of the minuend. The borrow may be indicated as shown below:

Now observe the following method of borrowing across more than one column in the example, 10002 - 12:

Example 1

Example 2

Example 3