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". Binary, or base 2, is one of many possible Number Systems.
A number written in the system can be denoted by following it with a subscript 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 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:
- Current digit is the end digit
- Change the current digit
- If current digit = 1
- Then:
- Shift current digit to away from the end digit
- Go to step 2
- Else:
- You're done.
- Then:
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 | |
