Binary system

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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:

DecimalBinary
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

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