128 (number)

128 (one hundred [and] twenty-eight) is the natural number following 127 and preceding 129.

← 127 129 → 128
← 120 121 122 123 124 125 126 127 128 129 → List of numbers — Integers ← 100 110 120 130 140 150 160 170 180 190 →
Cardinal	one hundred [and] twenty-eight
Ordinal	128th (one hundred [and] twenty-eighth)
Numeral system	128
Factorization	27
Divisors	1, 2, 4, 8, 16, 32, 64, 128
Roman numeral	CXXVIII
Binary	100000002
Octal	2008
Duodecimal	A812
Hexadecimal	8016

In mathematics

One hundred [and] twenty-eight is the seventh power of 2. It is the largest number which cannot be expressed as the sum of any number of distinct squares.^[1][2] But it is divisible by the total number of its divisors, making it a refactorable number.^[3]

The sum of Euler's totient function φ(x) over the first twenty integers is 128.^[4]

128 can be expressed by a combination of its digits with mathematical operators thus 128 = 2^{8 - 1}, making it a Friedman number in base 10.^[5]

A hepteract has 128 vertices.

128 is the only 3-digit number that is a 7th power. 2 to the 7th power.

In bar codes

• Code 128 is a Uniform Symbology Specification (USS Code 128) alphanumeric bar code that encodes text, numbers, numerous functions, and designed to encode all 128 ASCII characters (ASCII 0 to ASCII 128.), as used in the shipping industry.
• International Symbology Specification Code (ISS Code) 128 is the USS Code for encoding of extended non-English ASCII characters

• Subdivisions include:
  • 128A (0-9, A-Z, ASCII control codes, special characters)
  • 128B (0-9, A-Z, a-z, special characters)
  • 128C (00-99 numeric characters)
  • GS1-128 application standard of the GS1 implementation using the Code 128 barcode specification
  • ISBT 128 system for blood product labeling for the International Society of Blood Transfusion

In computing

• 128-bit key size encryption for secure communications over the Internet
  • IPv6 uses 128-bit (16-byte) addresses
  • Any bit with a binary prefix is 128 bytes of a lesser binary prefix value, such as 1 gibibit is 128 mebibytes
  • 128-bit integers, memory addresses, or other data units are those that are at most 128 bits 16 octets wide

• ASCII includes definitions for 128 characters (33 non-printing characters, mostly obsolete control characters that affect how text is processed, and 94 printable)
• CAST-128 is a block cipher used in a number of products, notably as the default cipher in some versions of GPG and PGP.
• Graphics cards have a 128-bit or 256-bit data bus to memory.
• Atari 2600 consoles have 128 bytes of memory
• Sony's PlayStation 2 Emotion Engine CPU has two 128-bit vector units
• Macintosh 128K was the original Apple Macintosh personal computer released in 1984
• Laser 128 released by VTech was a clone of the Apple II released in 1984
• Commodore 128 home/personal computer which had a 128 KB of memory released in 1985
• Enterprise Zilog Z80 home computer released in 1985
• Jane 128 was a GUI-based integrated software package for the Commodore 128 personal computer released in 1985
• RIVA 128 (Real-time Interactive Video and Animation accelerator) was one of the first consumer graphics chips to integrate 3D and video acceleration in 1997
• Super Mario 128 is a cancelled Nintendo game, though many elements were included in Super Mario Galaxy and Pikmin.

In the military

• USNS Mission San Luis Rey (T-AO-128) was a United States Navy Mission Buenaventura class fleet oiler fleet oilers during World War II
• USS Arenac (APA-128) was a United States Navy Haskell-class attack transport during World War II
• USS Cavallaro (APD-128) was a United States Navy Crosley-class high speed transport ship
• USS Leonis (AK-128) was a United States Navy Crater-class cargo ship during World War II
• USS Velocity (AM-128) was a United States Navy Auk-class minesweeper which removed mines from minefields laid in the water

In transportation

• A small car manufactured by Fiat, the Fiat 128 from 1969 to 1985. SEAT 128 was a 2-door coupé version of the car
• The BMW 128i convertible
• Massachusetts Route 128, Boston's inner beltway, approximately 10-mile radius.
• Route 128 Station is a stop on the Massachusetts Bay Transportation Authority Attleboro/Providence MBTA Commuter Rail line in Westwood, Massachusetts
• STS-128 is a currently flying Space Shuttle Discovery mission to the International Space Station for 2009

In other fields

One hundred [and] twenty-eight is also:

• The year AD 128 or 128 BC
• 128 AH is a year in the Islamic calendar that corresponds to 745 – 746 CE
• 128 Nemesis is a main belt asteroid
• Ross 128 is a red dwarf star, eleventh closest star system to the Solar System
• 128P/Shoemaker-Holt is a periodic comet in the Solar system
• The atomic number of unbioctium, an element yet to be discovered.
• The number of musical instruments specified in General MIDI. Sometimes they are numbered 0 to 127 and sometimes they are numbered 1 to 128.
• 128 film, a film format
• Sonnet 128 by William Shakespeare
• In music, a hundred twenty-eighth note is a note played for 1/128 of the duration of a whole note
• 128 is a sacred number honored by Beans for many generations^{[citation needed]}

See also

• 128th (disambiguation)
• List of highways numbered 128
• United Nations Security Council Resolution 128

Notes

1. ^ Sprague, R. (1948), "Über Zerlegungen in ungleiche Quadratzahlen", Math. Z. 51: 289–290, doi:10.1007/BF01181594, MR0027285 
2. ^ OEIS:A001422. Similarly, the largest numbers that cannot be expressed as sums of distinct cubes and fourth powers, respectively, are 12758 and 5134240 (sequence A001661 in OEIS).
3. ^ OEIS:A033950.
4. ^ OEIS:A002088.
5. ^ OEIS:A036057.

References

• Wells, D. The Penguin Dictionary of Curious and Interesting Numbers London: Penguin Group. (1987): 138

External links

• Code 128 specification at OpenBarcode.org