Binary system

The binary system is a way of representing numbers in base 2, i.e. using only the digits 0 and 1. The term 'Binary' means composed of two parts and comes from the Latin, originally meaning "two by two".

A number written in the system can be denoted by following it with a subscipt 2, i.e. ₂. Each digit represents the number of a power of 2 in the complete number, similarly to in the decimal system, where each digit represents the number of a power of 10. The power is defined by the number of digits in the number from right to left through the digit, minus 1, e.g. 100₂, where the digit 1 is the third digit from the right, and thus represents 2², or 4. While it is generally impractical for human use, it is the mainstay of modern computing. A binary system is also used in electronics, which commonly uses 0 to mean "no voltage is present" 1 to mean "a voltage is present". Binary notation is used in circumstances in which a a thing is in one of two possible conditions and no other condition is possible; the switch is on or the switch is off, the page has data on it or the page has no data.

To increment a binary number, follow this rule:

1. Current digit is the end digit
2. Change the current digit
3. If current digit = 1
   1. Then:
      1. Shift current digit to away from the end digit
      2. Go to step 2
   2. Else:
      1. You're done.

The first 16 binary digits:

Decimal	Binary
0	0
1	1
2	10
3	11
4	100
5	101
6	110
7	111
8	1000
9	1001
10	1010
11	1011
12	1100
13	1101
14	1110
15	1111
16	10000

See Also

• Binary Code
• Binary Function
• Binary Compound

External links

• A binary numbering game
• How to make binary numbers