Prefixes Binary Multiplies

Overview

Engineering reference data for Prefixes Binary Multiplies in basics.

Key Formulas

Ohm's Law

$V = IR$

Voltage = Current × Resistance.

Newton's Second Law

$F = ma$

Force = mass × acceleration.

Conservation of Energy

$E_{in} = E_{out} + \Delta E_{stored}$

Energy balance.

Variables

Symbol	Description	Unit
$V$	Voltage	V
$I$	Current	A
$R$	Resistance	Ω
$F$	Force	N
$m$	Mass	kg
$a$	Acceleration	m/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

Binary vs. SI Prefix Comparison

Conversion Formulas

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

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

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

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

Therefore, the conversion factor between binary and decimal is:

$\frac{\text{Binary value}}{\text{SI value}} = \frac{2^{10n}}{10^{3n}} = \left(\frac{2^{10}}{10^3}\right)^n = \left(\frac{1024}{1000}\right)^n$

References

• Original Source