128 (number)

← 127 128 129 →
← 120 121 122 123 124 125 126 127 128 129 → List of numbers; Integers; ← 0 100 200 300 400 500 600 700 800 900 →
Cardinal	one hundred twenty-eight
Ordinal	128th; (one hundred twenty-eighth)
Factorization	27
Divisors	1, 2, 4, 8, 16, 32, 64, 128
Greek numeral	ΡΚΗ´
Roman numeral	CXXVIII
Binary	100000002
Ternary	112023
Senary	3326
Octal	2008
Duodecimal	A812
Hexadecimal	8016

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

In mathematics

128 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] However, 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 (2⁷).

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 127), as used in the shipping industry.
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

All 128 possible states of the seven-segment display.

Seven-segment displays have 128 possible states.
ASCII includes definitions for 128 characters (33 non-printing characters, mostly obsolete control characters that affect how text is processed, and 94 printable)
A 128-bit integer can represent up to 3.40282366...e+38 values (2¹²⁸ $=$ 340,282,366,920,938,463,463,374,607,431,768,211,456).
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, 256-bit, or 512-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, the original Apple Macintosh personal computer released in 1984
Laser 128, an Apple II clone released in 1984
Commodore 128, a home/personal computer which had a 128 KB of memory released in 1985
Enterprise 128 Zilog Z80, a home computer released in 1985
Jane 128, a GUI-based integrated software package for the Commodore 128 personal computer released in 1985
RIVA 128 (Real-time Interactive Video and Animation accelerator), one of the first consumer graphics chips to integrate 3D and video acceleration in 1997
Super Mario 128, 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), a United States Navy Mission Buenaventura-class fleet oilers during World War II
USS Arenac (APA-128), a United States Navy Haskell-class attack transport during World War II
USS Cavallaro (APD-128), a United States Navy Crosley-class high speed transport
USS Leonis (AK-128), a United States Navy Crater-class cargo ship during World War II
USS Velocity (AM-128), a United States Navy Auk-class minesweeper which removed naval mines laid in the water

In transportation

Fiat 128, a small car manufactured by Fiat from 1969 to 1985.
SEAT 128, a 2-door coupe version of the Fiat 128
The BMW 128i convertible
128 is the number of many roads, including Massachusetts Route 128, Boston's inner beltway.
Route 128 Station is a stop on the Massachusetts Bay Transportation Authority Attleboro/Providence MBTA Commuter Rail line in Westwood, Massachusetts
STS-128 was a Space Shuttle Discovery mission to the International Space Station in 2009

In other fields

One hundred [and] twenty-eight is also:

The year AD 128 or 128 BC
128 AH, a year in the Islamic calendar that corresponds to 745 – 746 CE
128 Nemesis, a main-belt asteroid
Ross 128, a red dwarf star, the eleventh closest star system to the Solar System
128P/Shoemaker-Holt, 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
The number of US fluid ounces in a US gallon

Notes

^ Sprague, R. (1948), "Über Zerlegungen in ungleiche Quadratzahlen", Math. Z., 51 (3): 289–290, doi:10.1007/BF01181594, MR 0027285, S2CID 123515191
^ 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 the OEIS).
^ OEIS:A033950.
^ OEIS:A002088.
^ 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

[1] Sprague, R. (1948), "Über Zerlegungen in ungleiche Quadratzahlen", Math. Z., 51 (3): 289–290, doi:10.1007/BF01181594, MR 0027285, S2CID 123515191

[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 the OEIS).

[3] OEIS:A033950.

[4] OEIS:A002088.

[5] OEIS:A036057.

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