Difference between revisions of "Binary system"
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To increment a binary number, follow this rule: | To increment a binary number, follow this rule: | ||
| − | 1. Current digit is the end digit | + | 1. Current digit is the end digit |
| − | 2. Change the current digit | + | 2. Change the current digit |
| − | 3. If current digit = 1 | + | 3. If current digit = 1 |
| − | 4. Then: | + | 4. Then: |
| − | 4a.Shift current digits to away from the end digit | + | 4a.Shift current digits to away from the end digit |
| − | 4b.Goto step 2 | + | 4b.Goto step 2 |
| − | 5: Else: | + | 5: Else: |
| − | 5a:You're done. | + | 5a:You're done. |
A more concrete example can be found here: | A more concrete example can be found here: | ||
| Line 16: | Line 16: | ||
The first 16 binary digits: | The first 16 binary digits: | ||
| − | :0 | + | {|style="text-align:center" |
| − | + | !Decimal!!Colspan=2 |Binary | |
| − | + | |- | |
| − | + | |width=50px|0 | |
| − | + | |width=50px align="right"|0 | |
| − | + | |width=10px| | |
| − | + | |- | |
| − | + | |1 | |
| − | + | |align="right"|1 | |
| − | + | |- | |
| − | + | |2 | |
| − | + | |align="right"|10 | |
| − | + | |- | |
| − | + | |3 | |
| − | + | |align="right"|11 | |
| − | + | |- | |
| − | + | |4 | |
| + | |align="right"|100 | ||
| + | |- | ||
| + | |5 | ||
| + | |align="right"|101 | ||
| + | |- | ||
| + | |6 | ||
| + | |align="right"|110 | ||
| + | |- | ||
| + | |7 | ||
| + | |align="right"|111 | ||
| + | |- | ||
| + | |8 | ||
| + | |align="right"|1000 | ||
| + | |- | ||
| + | |9 | ||
| + | |align="right"|1001 | ||
| + | |- | ||
| + | |10 | ||
| + | |align="right"|1010 | ||
| + | |- | ||
| + | |11 | ||
| + | |align="right"|1011 | ||
| + | |- | ||
| + | |12 | ||
| + | |align="right"|1100 | ||
| + | |- | ||
| + | |13 | ||
| + | |align="right"|1101 | ||
| + | |- | ||
| + | |14 | ||
| + | |align="right"|1110 | ||
| + | |- | ||
| + | |15 | ||
| + | |align="right"|1111 | ||
| + | |- | ||
| + | |16 | ||
| + | |align="right"|10000 | ||
| + | |} | ||
[[Category:Mathematics]] | [[Category:Mathematics]] | ||
Revision as of 17:06, July 14, 2007
The binary system is a way of representing numbers in base 2, i.e. using only the digits 0 and 1. While it is impractical for human use, it is the mainstay of modern computing.
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 4. Then: 4a.Shift current digits to away from the end digit 4b.Goto step 2 5: Else: 5a:You're done.
A more concrete example can be found here: http://woodgears.ca/marbleadd/index.html
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 | |