Numeric

Resources around numeric data.

Introduction

Numeric data and numbers can exist is a number of different flavors, some examples of terminology used include:

  • integers, integer, short integer, long integer
  • signed or unsigned
  • floating point, decimal, short decimal
  • number

In essence it's the particular computing environment that defines which types exist and how to use these.

Examples:

There are many specific resources on the Internet for all sorts of considerations of data and this page only focuses on a small subset of particularly important details in regard to data communications and machine-to-machine exchange of data.

See also section on Speed for more examples of, sometimes confusing, use of bits and bytes, kilo, mega, ...

Bits, Bytes, and Prefixes

To be very clear, as abbreviations in this field can be very confusing, absolutely also for professionals who work with this daily and are not clear on what they absolutely mean (especially kilo, mega, etc when talking bytes).

For instance, in general (the whole wide world, based on the SI system):

  • Base 10, Decimal system
    • a 'k' means a 'kilo' and a factor of 1,000 (103),
    • a 'M' means a 'mega' and a factor of 1,000,000 (106), and so on.

But, in the digital world it gets a bit messier, including on which datacom layer someone is talking...

  • In some cases, prefixes are used as per above (the international SI standard) but in other cases:
  • Base 2, Binary system:
    • a 'k' is still interpreted as 'kilo' but using a factor of 1,024 (210),
    • a 'M' is still interpreted as 'mega' but using a factor of 1,048,576 (220), and so on.
  • When discussion transmission speeds on the lowest level, Physical, people almost always think and mean using SI (base 10), a kilo is 1000.
  • When discussion transfer speeds on highest level, Application, it very much depend on who's talking, what they are looking at. Some examples:
    • When someone talks about content of a CD they are - knowingly or unknowingly - implying Base 2, 700 MB means 700x10242 bytes.
    • When someone talks about content of a DVD they are - knowingly or unknowingly - more likely implying Base 10, 4.7 GB means 4.7 x 10003 bytes.

Units

Name Symbol What Values
bit b Smallest unit, one bit is either a zero or a one - lowest component in computers 2: 0 or 1
nibble (none) 4 bits, one hexadecimal number 16: 0-15, (0-9,A-F hex)
byte B Unit, 8 bits forms a byte. Always. 256: 0-255

Unfortunately, people are NOT as stringent using 'b' for bits and 'B' for bytes and sometimes this is also mixed up - be careful.

 

Prefixes

    General Use, SI, Base 10, All Applications Digital World, Base 2 ,Alt. Interpretation
Prefix
Name
Symbol
[SI]
Factor
[SI, base 10]
Power
[SI, base 10]
Base 2 Base 1024 Prefix
[IEC]
Symbol
[IEC]
- 1 100 (10000) 20 (10240) 1
c: 1
-
kilo k 1 000 103 (10001) 210 (10241) s: 1024 kibi Ki
mega M 1 000 000 106 (10002) 220 (10242) s: 1048576 mebi Mi
giga G 1 000 000 000 109 (10003) 230 (10243) s: 1073741824 gibi Gi
tera T 1 000 000 000 000 1012 (10004) 240 (10244) s: 1099511627776 tebi Ti
peta P 1 000 000 000 000 000 1015 (10005) 250 (10245) s: 1125899906842624 pebi Pi
exa E 1 000 000 000 000 000 000 1018 (10006) 260 (10246) s: 1152921504606846976 exbi Ei
zetta Z 1 000 000 000 000 000 000 000 1021 (10007) 270 (10247) s: 1180591620717411303424 zebi Zi
yotta Y 1 000 000 000 000 000 000 000 000 1024 (10008) 280 (10248) s: 1208925819614629174706176 yobi Yi
undef 1 000 000 000 000 000 000 000 000 000 1027 (10009) 290 (10249) 1.2379400392854E+27
c: 1 237 940 039 285 380 274 899 124 224

 

Lowercase 'k' and Capital 'K'

Case   Name Acceptance Rec.Use Notes
Upper K Kelvin Universally accepted standard Yes Temperature in unit kelvin. Unit, 'K', note that use is NOT "degree Kelvin" (symbolically °K) but simply "kelvin" (symbol K).
Lower k kilo Universally accepted standard Yes Prefix (SI) for kilo, factor of 1,000 (103), 'decimal kilo'
Alt.          
Upper K kilo (base 2) Some computing No! Prefix for factor 1,024 (210), 'binary kilo' (JEDEC)
Lower k kilo (base 2) Some computing No! Prefix for factor 1,024 (210), 'binary kilo'. Use newer 'kibi', 'Ki', instead of 'k'
Lower k kilo (base 10) Some computing Yes Prefix for factor 1,000 (103), 'decimal kilo'

wikipedia JEDEC memory standards: Unit prefixes for semiconductor storage capacity

Example In (e.g.) Interpretation In Modern Standard
10 KB MS Windows File Explorer Base 2: 10 x (210), 10240 bytes (B) 10 KiB (kibibytes)
10 kB IT HW, Mac OS Finder, Base 10: 10 x (10003), 10000 bytes (B) (<-, as example)
10 KiB Some Linux Base 2: 10 x (210), 10240 bytes (B) (<-, as example)
10 kiB incorrect prefix    
10 kb (E.g. when talking speeds Base 10: 10 x (10003), 10000 bits (b) (<-, as example)
10 Kb poor use When talking bits, it can be even harder to determine if intention is base 2 'kilo' (kibi!) or base 10 kilo. Either use 'kb' (kilobit,1000) or 'Kib' (kibibit, 1024)
10 Kib (E.g. when talking speeds Base 2: 10 x (210), 10240 bits (b) (<-, as example)

 

 

 

Mixed and Confusing Use of Prefixes in IT

 

Area Base Units (e.g.) Actual Interpretation
Memory, volatile, RAM Base 2 'MB',
'GB'
'MB' = 220,10242, = MiB
'GB' = 230, 10243, = GiB
Hard drives (trad., mechanical) Base 10 'GB', 'TB' 'GB' = 106,10009,
'TB' = 109, 100012.
Diskettes Mix 'MB' A '1.44 MB' disc actually holds 1,440 KiB, 1440 x 1024, 1474560 bytes, ~1.41 MiB or ~1.47 MB10. (wikipedia: Floppy_disk)
Compact Disc, CD Base 2 'MB' A '700 MB' capacity disc can store around 700 MiB, 737 MB10. (wikipedia: Compact_disc, wikipedia: CD-R)
DVDs Base 10 'GB' A '4.7 GB (single-sided, single-layer)' DVD-R holds 4,707,319,808 bytes, around 4.4 GiB. (wikipedia: DVD)
USB Flash drive Base 10 'GB' A '32 GB' stick holds around 32,000,000,000 bytes, around 29.8 GiB. (wikipedia: DVD)

http://swedeteam.com/kibi/

https://en.wikipedia.org/wiki/Binary_prefix#Usage_notes

http://swedeteam.com/kibi/calc/

Hard specifications, physical capacity, as specified by hardware manufacturers is one thing, how presented in software can be something completely different. Example

By / Where Shown What you see (e.g.) Base Comments
By manufacturer "32 GB, 32 billion bytes" 10 (A modern 32 GB USB stick), as specifiied by manufacturer, on box, on web site, around* 32,000,000,000 bytes. *) variations due to technology and manufacturing. (32 bilion bytes, 32*109 / 230 ≈ 29.8 gibibytes, GiB)
In Mac OS pre 10.6, Finder "29.8 GB" 2 Uses older interpretation (32*109 / 230 ≈ 29.8)
In Mac OS 10.6 and later, Finder "32 GB" 10 Conforms to SI, decimal system
In MS Windows, File Explorer "29.8 GB" 2 Uses older interpretation
Modern Linux file managers "29.8 GiB" 10 Uses IEC, thus also conforms to SI

Why does Explorer use the term KB instead of KiB? blogs.msdn.microsoft.com/oldnewthing/20090611-00/?p=17933

google.com/search?q=ms+windows+megabyte