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Difference between revisions of "Bit level"
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| − | Since [[Mersenne number]]s are by nature [[binary]], it makes sense to perform calculations on them directly in binary. When searching for [[factor]]s of Mersennes [[Prime95]] and some other [[:Category:Factoring program|factoring program]]s use and report '''bit level''' as starting and stopping points, bit meaning '''bi'''nary dig'''it''', others use the | + | Since [[Mersenne number]]s are by nature [[binary]], it makes sense to perform calculations on them directly in binary. When searching for [[factor]]s of Mersennes [[Prime95]] and some other [[:Category:Factoring program|factoring program]]s use and report '''bit level''' as starting and stopping points, bit meaning '''bi'''nary dig'''it''', others use the '''[[value k|{{Vk}}]]''' value. |
Every number can be represented in either binary or decimal. For each new [[digit]] added to a number binaries are twice as large, while decimals are ten times as large. A number that has 70 binary digits (all 1's) would be at the 70 bit level. To check for factors from one bit level to the next (e.g. from 70 to 71) takes twice as much work (there are two times as many potential factors to check.) | Every number can be represented in either binary or decimal. For each new [[digit]] added to a number binaries are twice as large, while decimals are ten times as large. A number that has 70 binary digits (all 1's) would be at the 70 bit level. To check for factors from one bit level to the next (e.g. from 70 to 71) takes twice as much work (there are two times as many potential factors to check.) | ||
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|- | |- | ||
| align="right" | 1111 1111 1111 1111 | | align="right" | 1111 1111 1111 1111 | ||
| − | | align="right" | | + | | align="right" | {{Num|65535}} |
| 16 | | 16 | ||
|- | |- | ||
| align="right" | 1 0000 1001 0011 0010 | | align="right" | 1 0000 1001 0011 0010 | ||
| − | | align="right" | | + | | align="right" | {{Num|67890}} |
| 16.05 | | 16.05 | ||
|- | |- | ||
| align="right" | 1 1111 1111 1111 1111 | | align="right" | 1 1111 1111 1111 1111 | ||
| − | | align="right" | | + | | align="right" | {{Num|131071}} |
| 17 | | 17 | ||
|- | |- | ||
| align="right" | 1010 1010 1010 1010 1010 1010 1010 1010 | | align="right" | 1010 1010 1010 1010 1010 1010 1010 1010 | ||
| − | | align="right" | | + | | align="right" | {{Num|2863311530}} |
| 31.42 | | 31.42 | ||
|- | |- | ||
| align="right" | 1111 1111 0000 0000 0000 0000 0000 0000 | | align="right" | 1111 1111 0000 0000 0000 0000 0000 0000 | ||
| − | | align="right" | | + | | align="right" | {{Num|4278190080}} |
| 31.99 | | 31.99 | ||
|} | |} | ||
[[Category:Math]] | [[Category:Math]] | ||
[[Category:Factorization]] | [[Category:Factorization]] | ||
Latest revision as of 18:47, 14 December 2023
Since Mersenne numbers are by nature binary, it makes sense to perform calculations on them directly in binary. When searching for factors of Mersennes Prime95 and some other factoring programs use and report bit level as starting and stopping points, bit meaning binary digit, others use the k value.
Every number can be represented in either binary or decimal. For each new digit added to a number binaries are twice as large, while decimals are ten times as large. A number that has 70 binary digits (all 1's) would be at the 70 bit level. To check for factors from one bit level to the next (e.g. from 70 to 71) takes twice as much work (there are two times as many potential factors to check.)
While at first bit level may appear to be quantum in nature, bit levels such as 75.3 are often seen.
Examples
| Binary | Decimal | Bit level |
|---|---|---|
| 1111 1111 1111 1111 | 65,535 | 16 |
| 1 0000 1001 0011 0010 | 67,890 | 16.05 |
| 1 1111 1111 1111 1111 | 131,071 | 17 |
| 1010 1010 1010 1010 1010 1010 1010 1010 | 2,863,311,530 | 31.42 |
| 1111 1111 0000 0000 0000 0000 0000 0000 | 4,278,190,080 | 31.99 |
