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Conversion: bits and bytes

1 byte are 8 bits or 1 B = 8 b

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bits (b)
bytes (B)
kibibytes (KiB)
mebibytes (MiB)
gibibytes (GiB)
tebibytes (TiB)
New standard
In January 1999, the International Electrotechnical Commission introduced in an addendum to IEC 60027-2 the prefixes kibi- (kibibyte), mebi-, gibi-, etc., and the symbols Ki, Mi, Gi, etc. to specify binary multiples of a quantity and eliminate the ambiguity with their SI meanings. Kibibit sounds a bit funny. Here it is the new standard:

Name Symbol Before 1998 standardization Name After the standardization
bit b  1 bit   = 1 bit bit  1 b   = 1 bit
byte B  1 B   = 8 bit byte  1 B   = 8 bit
kilobit kbit / kb  1 kbit   = 1024 b = bit kilobit  1 kb   = 1000 b
kibibit Kibit         kibibit  1 Kib   = 1024 b
kilobyte kB  1 kB   = 1024 B = Byte kilobyte  1 kB   = 1000 B
kibibyte KiB         kibibyte  1 KiB   = 1024 B
megabit Mbit  1 Mbit   = 1024 kb megabit  1 Mb   = 1000 kb
mebibit Mibit / Mib         mebibit  1 Mib   = 1024 Kib
megabyte MB  1 MB   = 1024 kB megabyte  1 MB   = 1000 kB
mebibyte Mibit / MiB         mebibyte  1 MiB   = 1024 KiB
gigabit Gbit / Gb  1 Gbit   = 1024 Mb gigabit  1 Gb   = 1000 MB
gibibit Gibit / Gib         gibibit  1 Gib   = 1024 MiB
gigabyte GB  1 GB   = 1024 MB gigabyte  1 GB   = 1000 MB
gibibyte GiB         gibibyte  1 GiB   = 1024 MiB
terabyte TB  1 TB   = 1024 GB terabyte  1 TB   = 1000 GB
tebibyte TiB         tebibyte  1 TiB   = 1024 GiB
petabyte PB  1 PB   = 1024 TB petabyte  1 PB   = 1000 TB
pebibyte PiB         pebibyte  1 PiB   = 1024 TiB
exabyte EB  1 EB   = 1024 PB exabyte  1 EB   = 1000 PB
exbibyte EiB         exbibyte  1 EiB   = 1024 PiB
zettabyte ZB  1 ZB   = 1024 EB zettabyte  1 ZB   = 1000 EB
zebibyte ZiB         zebibyte  1 ZiB   = 1024 EiB
yottabyte YB  1 YB   = 1024 ZB yottabyte  1 YB   = 1000 ZB
yobibyte YiB         yobibyte  1 YiB   = 1024 ZiB

    Old Definitions:
  • 1 kb  =  (210)   bits = 1 024 b
  • 1 MB = (210)2 Bytes = 1 048 576 B

To make the SI prefixes universal and to avoid confusion in the future, International Electrotechnical Commission (IEC), the leading international organization for worldwide standardization in electrotechnology, approved in December 1998 standard names and symbols of prefixes for binary multiples to be used in the fields of data processing and transmission. The prefixes are:

Name Prefix Symbol Power Factor
kilobinary kibi Ki (210)1 1 024
megabinary mebi Mi (210)2 1 048 576
gigabinary gibi Gi (210)3 1 073 741 824
terabinary tebi Ti (210)4 1 099 511 627 776
petabinary pebi Pi (210)5 1 125 899 906 842 624
exabinary exbi Ei (210)6 1 152 921 504 606 846 976

Name Prefix Symbol Power Factor
kilo kilo k   103 1 000
mega mega M   106 1 000 000
giga giga G   109 1 000 000 000
tera tera T 1012 1 000 000 000 000
peta peta P 1015 1 000 000 000 000 000
exa exa E 1018 1 000 000 000 000 000 000

It is suggested that in English, the first syllable of the name of the binary-multiple prefix should be pronounced in the same way as the first syllable of the name of the corresponding SI prefix, and that the second syllable should be pronounced as "bee." Examples and comparisons with SI prefixes:
1 Kib = 210 bit = 1024 bit,
1 kb = 103 bit = 1000 bit,
1 MiB = 220 B = 1 048 576 B,
1 MB = 106 B = 1 000 000 B,
1 GiB = 230 B = 1 073 741 824 B,
1 GB = 109 B = 1 000 000 000 B.
Based on the new definitions, the SI prefixes, k, M, and G, are back to their original meaning of
1 000, 1 000 000, and 1 000 000 000, respectively. The commonly known binary prefixes are written as Ki, Mi, and Gi and pronounced as kibi, mebi, and gibi, respectively.

New Definitions:

  • 1 kilo-bit = 1 kb = 103 bits = 1 000 b
    •  
  • 1 kilobinarybit = 1 kibibit = 1 Kib = 210 bits = 1 024 b
    •  
  • 1 megabyte = 1 MB = 106 Bytes = 1 000 000 B
    •  
  • 1 megabinarybyte = 1 mebibyte = 1 MiB = (210)2 B = 1 048 576 B

    • The IEEE Standards Board decided that IEEE standards will be using the conventional, internationally adopted, definitions of the base-ten SI prefixes, except that the base-two definition may be used if such usage is explicitly pointed out on a case-by-case basis.

    Conversion: Transfer rates and bandwidths

    byte = the well-established information measure unity

    bit = the well-established data transfer unity

    1 kilobit = 1 000 bits
    1 megabit = 1 000 000 bits

    Data of the hard disk are counted in kilobytes, however the transfer data rates are in kilobits.

    Conclusion: A 56 k modem = 56 000 bits needs for transferring of
    56 k data = 458 753 bits not 1 second, but at least 8.2 seconds.
    This is confusing and you must always bear it in mind, when calculating transfer rates.

    Rule of thumb : KByte of the data / seconds = transfer rate.

    Connection Theoretical
    rate in kb    		 Optimal
    rate in KB    		 Probable
    rate in KB
    14.4 modem 14.4 kb/s 1.2 KB/s   1 KB/s
    28.8 modem 28.8 kb/s 2.4 KB/s   2 KB/s
    33.6 modem 33.6 kb/s    3 KB/s 2.5KB/s
    56 k  modem    53 kb/s 4.8 KB/s   4 KB/s
    Single ISDN    64 kb/s 6 KB/s   5 KB/s
    Dual ISDN 128 kb/s 12 KB/s 10 KB/s
    DSL - light 384 kb/s 35 KB/s 30 KB/s
    DSL 1024 kb/s 125 KB/s 90 KB/s
    DSL 2048 kb/s 250 KB/s 180 KB/s
    DSL 3072 kb/s 500 KB/s 360 KB/s
    T1 1,54 Mb/s 150 KB/s 50 KB/s
    Cable modem   6 Mb/s 300 KB/s 50 KB/s
    Intranet / LAN 10 Mb/s 350 KB/s 35 KB/s
    100 base-T Lan 100 Mb/s 500 KB/s 50 KB/s

    The new IEC Standard
    Name bit       byte  
    bit bit 0 or 1
    byte B 8 bits
    kibibit (binary) Kib 1024 bits
    kilobit (decimal) kb 1000 bits
    kibibyte (binary) KiB 1024 bytes
    kilobyte (decimal) kB 1000 bytes
    megabit (decimal) Mb 1000 kilobits
    mebibyte (binary) MiB 1024 kibibytes
    megabyte (decimal) MB 1000 kilobytes
    gigabit (decimal) Gb 1000 megabits
    gibibyte (binary) GiB 1024 mebibytes
    gigabyte (decimal) GB 1000 megabytes
    terabit (decimal) Tb 1000 gigabits
    tebibyte (binary) TiB 1024 gibibytes
    terabyte (decimal) TB 1000 gigabytes
    petabit (decimal) Pb 1000 terabits
    pebibyte (binary) PiB 1024 tebibytes
    petabyte (decimal) PB 1000 terabytes
    exabit (decimal) Eb 1000 petabits
    exbibyte (binary) EiB 1024 pebibytes
    exabyte (decimal) EB 1000 petabytes

    In data communications the metric definition of a kilobyte (1000 bytes per kilobyte) is
    correct. The binary definition of a kilobyte (1024 bytes per kilobyte) is used in areas such
    as data storage (harddisk, memory), but not for expressing bandwidth and throughput.

    File Storage Capacity by Bits and Bytes
      bit byte kibibyte mebibyte gibiyte
    bit 1 0.125 0.000122070312 1.192092895×10-7 1.16415321875×10-10
    byte 8 1 0.0009765625 9.53674316×10-7 9.31322575×10-10
    kibibyte 8 192 1 024 1 0.0009765625 9.53674316×10-7
    mebibyte 8 388 608 1 048 576 1 024 1 0.0009765625
    gibibyte 8 589 934 592 1 073 741 824 1 048 576 1 024 1
    tebibyte 8 796 093 022 208 1 099 511 627 776 1 073 741 824 1 048 576 1 024
    pebibyte 9 007 199 254 740 990 1 125 899 906 842 624 1 099 511 627 776 1 073 741 824 1 048 576
    exbiyte 9 223 372 036 854 780 000 1 152 921 504 606 846 976 1 125 899 906 842 624 1 099 511 627 776 1 073 741 824
    zebibyte 9 444 732 965 739 290 000 000 1 180 591 620 717 411 303 424 1 152 921 504 606 846 976 1 125 899 906 842 624 1 099 511 627 776

    CD: 2 × 44 100 × 16 = 1.4112 Mb/s : 8 b/B = 176.4 kb/s
    2 × 44 100 × 20 = 1.764 Mb/s : 8 b/B = 220.5 kb/s
    2 × 44 100 × 24 = 2.1168 Mb/s : 8 b/B = 264.6 kb/s
    2 × 48 000 × 24 = 2.304 Mb/s : 8 b/B = 288.0 kb/s

    These words are generally not accepted.
    Units from Amendment 2 - International Standard IEC 60027-2

    Prefix Symbol Power Factor
    Yotta Y 1024 1 000 000 000 000 000 000 000 000
    Zetta Z 1021 1 000 000 000 000 000 000 000
    Exbi Ei 260 1 152 921 504 606 846 976
    Exa E 1018 1 000 000 000 000 000 000
    Pebi Pi 250 1 125 899 906 842 624
    Peta P 1015 1 000 000 000 000 000
    Tebi Ti 240 1 099 511 627 776
    Tera T 1012 1 000 000 000 000
    Gibi Gi 230 1 073 741 824
    Giga G 109 1 000 000 000
    Mebi Mi 220 1 048 576
    Mega M 106 1 000 000
    Kibi Ki 210 1 024
    Kilo k 103 1 000
    Reference unit 100 = 1  1

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