255 (number)

Last updated
254 255 256
Cardinal two hundred fifty-five
Ordinal 255th
(two hundred fifty-fifth)
Factorization 3 × 5 × 17
Greek numeral ΣΝΕ´
Roman numeral CCLV
Binary 111111112
Ternary 1001103
Senary 11036
Octal 3778
Duodecimal 19312
Hexadecimal FF16

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

Contents

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.

For example, 255 is the maximum value of

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.

Related Research Articles

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A computer number format is the internal representation of numeric values in digital device hardware and software, such as in programmable computers and calculators. Numerical values are stored as groupings of bits, such as bytes and words. The encoding between numerical values and bit patterns is chosen for convenience of the operation of the computer; the encoding used by the computer's instruction set generally requires conversion for external use, such as for printing and display. Different types of processors may have different internal representations of numerical values and different conventions are used for integer and real numbers. Most calculations are carried out with number formats that fit into a processor register, but some software systems allow representation of arbitrarily large numbers using multiple words of memory.

In number theory, a sphenic number is a positive integer that is the product of three distinct prime numbers. Because there are infinitely many prime numbers, there are also infinitely many sphenic numbers.

Two's complement is the most common method of representing signed integers on computers, and more generally, fixed point binary values. Two's complement uses the binary digit with the greatest place value as the sign to indicate whether the binary number is positive or negative. When the most significant bit is 1, the number is signed as negative; and when the most significant bit is 0 the number is signed as positive.

<span class="mw-page-title-main">Power of two</span> Two raised to an integer power

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256 is the natural number following 255 and preceding 257.

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<span class="mw-page-title-main">65,536</span> Natural number

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References

  1. Sloane, N. J. A. (ed.). "SequenceA007304(Sphenic numbers: products of 3 distinct primes.)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
  2. "PDF" (PDF). American Mathematical Society . Retrieved 12 March 2015.
  3. Hoovler, Evan. "The History of Annoying Side-Quests in Videogames Archived 2010-04-10 at the Wayback Machine ." GameSpy . 2009-12-04.
  4. Clewett, James. "255 and Pac-Man". Numberphile. 2007-17-11.