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# 255 (number)

## From Wikipedia, the free encyclopedia

 ← 254 255 256 →
Cardinaltwo hundred fifty-five
Ordinal255th
(two hundred fifty-fifth)
Factorization3 × 5 × 17
Greek numeralΣΝΕ´
Roman numeralCCLV
Binary111111112
Ternary1001103
Quaternary33334
Quinary20105
Senary11036
Octal3778
Duodecimal19312
HexadecimalFF16
VigesimalCF20
Base 367336

255 (two hundred [and] fifty-five) is the natural number following 254 and preceding 256.

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## In mathematics

Its factorization makes it a sphenic number.[1] Since 255 = 28 – 1, it is a Mersenne number[2] (though not a pernicious one), and the fourth such number not to be a prime number. It is a perfect totient number, the smallest such number to be neither a power of three nor thrice a prime.

Since 255 is the product of the first three Fermat primes, the regular 255-gon is constructible.

In base 10, it is a self number.

255 is a repdigit in base 2 (11111111), in base 4 (3333), and in base 16 (FF).

## In computing

255 is a special number in some tasks having to do with computing. This is the maximum value representable by an eight-digit binary number, and therefore the maximum representable by an unsigned 8-bit byte (the most common size of byte, also called an octet), the smallest common variable size used in high level programming languages (bit being smaller, but rarely used for value storage). The range is 0 to 255, which is 256 total values.

${\displaystyle 255=2^{8}-1={\mbox{FF}}_{16}=11111111_{2}}$

For example, 255 is the maximum value

The use of eight bits for storage in older video games has had the consequence of it appearing as a hard limit in many video games. For example, in the original The Legend of Zelda game, Link can carry a maximum of 255 rupees.[3] It was often used for numbers where casual gameplay would not cause anyone to exceed the number. However, in most situations it is reachable given enough time. This can cause many other peculiarities to appear when the number wraps back to 0, such as the infamous "kill screen" seen after clearing level 255 of Pac-Man.[4]

This number could be interpreted by a computer as −1 if a programmer is not careful about which 8-bit values are signed and unsigned, and the two's complement representation of −1 in a signed byte is equal to that of 255 in an unsigned byte.

## References

1. ^ "A007304". OEIS. Retrieved 12 March 2015.
2. ^ "PDF" (PDF). American Mathematical Society. Retrieved 12 March 2015. Cite web requires `|website=` (help)
3. ^ Hoovler, Evan. "The History of Annoying Side-Quests in Videogames Archived 2011-07-11 at the Wayback Machine." GameSpy. 2009-12-04.
4. ^ Clewett, James. "255 and Pac-Man." Numberphile. 2007-17-11.
This page was last edited on 20 August 2019, at 16:17
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