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Prefixes Binary Multiplies

Reference data and engineering information about prefixes binary multiplies for basics applications.

prefixesbinarymultiplies

Overview

Engineering reference data for Prefixes Binary Multiplies in basics.

Key Formulas

Ohm's Law

V=IRV = IR

Voltage = Current × Resistance.

Newton's Second Law

F=maF = ma

Force = mass × acceleration.

Conservation of Energy

Ein=Eout+ΔEstoredE_{in} = E_{out} + \Delta E_{stored}

Energy balance.

Variables

SymbolDescriptionUnit
VVVoltageV
IICurrentA
RRResistanceΩ
FFForceN
mmMasskg
aaAccelerationm/s²

Binary Prefixes

Binary prefixes are used in computing to denote powers of 2, as established by the IEC standard. These distinguish between binary multiples (kibi, mebi, gibi, etc.) and decimal SI prefixes (kilo, mega, giga, etc.) to avoid ambiguity in data processing and transmission.

Prefix Table

6 rows
IEC Binary Prefixes for Use in Data Processing and Transmission
Factor
Name
Symbol
Origin
Derivation
2^10kibiKikilobinary: (2^10)^1kilo: (10^3)^1
2^20mebiMimegabinary: (2^10)^2mega: (10^3)^2
2^30gibiGigigabinary: (2^10)^3giga: (10^3)^3
2^40tebiTiterabinary: (2^10)^4tera: (10^3)^4
2^50pebiPipetabinary: (2^10)^5peta: (10^3)^5
2^60exbiEiexabinary: (2^10)^6exa: (10^3)^6

Source: engineeringtoolbox.com

Binary vs. SI Prefix Comparison

6 rows
Comparison of Binary Multiples with SI Prefixes
Multiple
SI Equivalent
one kibibit1 Kibit = 2^10 bit = 1024 bit
one kilobit1 kbit = 10^3 bit = 1000 bit
one mebibyte1 MiB = 2^20 B = 1048576 B
one megabyte1 MB = 10^6 B = 1000000 B
one gibibyte1 GiB = 2^30 B = 1073741824 B
one gigabyte1 GB = 10^9 B = 1000000000 B

Source: engineeringtoolbox.com

Conversion Formulas

The relationship between binary and decimal representations can be expressed mathematically. For any binary prefix Xbi\text{Xbi} where n=1,2,3,…n = 1, 2, 3, \ldots:

1 Xbi-unit=210n base units1 \text{ Xbi-unit} = 2^{10n} \text{ base units}

The corresponding SI prefix X\text{X} (where X is kilo, mega, giga, etc.) follows:

1 X-unit=103n base units1 \text{ X-unit} = 10^{3n} \text{ base units}

Therefore, the conversion factor between binary and decimal is:

Binary valueSI value=210n103n=(210103)n=(10241000)n\frac{\text{Binary value}}{\text{SI value}} = \frac{2^{10n}}{10^{3n}} = \left(\frac{2^{10}}{10^3}\right)^n = \left(\frac{1024}{1000}\right)^n

References

Source: engineeringtoolbox.com