Difference between revisions of "Binary system"
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Revision as of 03:16, July 13, 2016
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:
- 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 | |
