Mebibytes to Gibibits conversion

How to convert mebibytes to gibibits?

A mebibyte (MiB) and a gibibit (Gib) are units used in computing for measuring data, based on binary (base 2) prefixes as defined by the International Electrotechnical Commission (IEC). These units are not the same as megabytes (MB) or gigabits (Gb) which are based on decimal (base 10) prefixes.

Conversion from Mebibytes to Gibibits (Base 2)

1 mebibyte (MiB) = $2^{20}$ bytes
1 gibibit (Gib) = $2^{30}$ bits
Since 1 byte = 8 bits: $1 \text{ MiB} = 2^{20} \text{ bytes} = 2^{20} \times 8 \text{ bits} = 2^{23} \text{ bits}$

$1 \text{ Gib} = 2^{30} \text{ bits}$

To convert from Mebibytes to Gibibits: $1 \text{ MiB} = \frac{2^{23} \text{ bits}}{2^{30} \text{ bits/ Gib}}$ $1 \text{ MiB} = \frac{1}{2^7} \text{ Gib}$ $1 \text{ MiB} = \frac{1}{128} \text{ Gib}$ $1 \text{ MiB} = 0.0078125 \text{ Gib}$

Conversion from Megabytes to Gigabits (Base 10)

While "megabyte" (MB) and "gigabit" (Gb) use base-10 prefixes, the process involves a straightforward decimal approach, but the unit conversion is fundamentally different from binary units.

1 megabyte (MB) = $10^6$ bytes
1 gigabit (Gb) = $10^9$ bits
Given that 1 byte = 8 bits: $1 \text{ MB} = 10^6 \text{ bytes} = 10^6 \times 8 \text{ bits} = 8 \times 10^6 \text{ bits}$

$1 \text{ Gb} = 10^9 \text{ bits}$

To convert from Megabytes to Gigabits: $1 \text{ MB} = \frac{8 \times 10^6 \text{ bits}}{10^9 \text{ bits/ Gb}}$ $1 \text{ MB} = 0.008 \text{ Gb}$

Real-World Examples for Other Quantities of Mebibytes

To provide some context, let's convert different sizes of mebibytes (MiB) to gibibits (Gib) for real-world applicability:

Example 1: 100 MiB $100 \text{ MiB} = 100 \times 0.0078125 \text{ Gib} = 0.78125 \text{ Gib}$

Example 2: 500 MiB $500 \text{ MiB} = 500 \times 0.0078125 \text{ Gib} = 3.90625 \text{ Gib}$

Example 3: 1024 MiB (which is 1 GiB) $1024 \text{ MiB} = 1024 \times 0.0078125 \text{ Gib} = 8 \text{ Gib}$

Summary

• 1 MiB (binary) equates to 0.0078125 Gib.
• 1 MB (decimal) equates to 0.008 Gb.

These conversions highlight the difference between binary and decimal units, emphasizing the importance of using the correct prefixes depending on the context.