Mebibytes per second to Gigabits per second conversion

How to convert mebibytes per second to gigabits per second?

To convert 1 Mebibyte per second (MiB/s) to Gigabits per second (Gbps), you need to understand the relationship between the different units of digital information. Here's a step-by-step explanation:

Definitions and Conversion Factors

1. Mebibyte (MiB): A Mebibyte is equal to $2^{20}$ bytes, or 1,048,576 bytes.
2. Gigabit (Gb): A Gigabit is equal to $10^9$ bits (base 10) or $2^30$ bits (base 2).

Note that 1 byte = 8 bits.

Conversion for Base 10 (Decimal System)

1. Calculate the amount of bytes in 1 MiB: $1 \text{ MiB} = 1,048,576 \text{ bytes}$

2. Convert bytes to bits: $1 \text{ MiB} = 1,048,576 \text{ bytes} \times 8 \text{ bits/byte} = 8,388,608 \text{ bits}$

3. Convert bits per second to Gigabits per second (base 10): $1 \text{ MiB/s} = \frac{8,388,608 \text{ bits/s}}{10^9} = 0.008388608 \text{ Gbps (base 10)}$

Conversion for Base 2 (Binary System)

1. Calculate the amount of bytes in 1 MiB: Same as above. $1 \text{ MiB} = 1,048,576 \text{ bytes}$

2. Convert bytes to bits: Same as above. $1 \text{ MiB} = 1,048,576 \text{ bytes} \times 8 \text{ bits/byte} = 8,388,608 \text{ bits}$

3. Convert bits per second to Gibibits per second (base 2): $1 \text{ MiB/s} = \frac{8,388,608 \text{ bits/s}}{2^{30}} = \frac{8,388,608 \text{ bits/s}}{1,073,741,824 \text{ bits}} = 0.0078125 \text{ Gibibits per second (GiBps)}$

Real World Examples

Here are some real-world examples for transferring data at different rates in MiB/s:

1. 10 MiB/s to Base 10 Gbps: $10 \text{ MiB/s} = 10 \times 0.008388608 \text{ Gbps} = 0.08388608 \text{ Gbps}$

2. 50 MiB/s to Base 10 Gbps: $50 \text{ MiB/s} = 50 \times 0.008388608 \text{ Gbps} = 0.4194304 \text{ Gbps}$

3. 100 MiB/s to Base 10 Gbps: $100 \text{ MiB/s} = 100 \times 0.008388608 \text{ Gbps} = 0.8388608 \text{ Gbps}$

4. 10 MiB/s to Base 2 Gibibits per second: $10 \text{ MiB/s} = 10 \times 0.0078125 \text{ GiBps} = 0.078125 \text{ GiBps}$

5. 50 MiB/s to Base 2 Gibibits per second: $50 \text{ MiB/s} = 50 \times 0.0078125 \text{ GiBps} = 0.390625 \text{ GiBps}$

6. 100 MiB/s to Base 2 Gibibits per second: $100 \text{ MiB/s} = 100 \times 0.0078125 \text{ GiBps} = 0.78125 \text{ GiBps}$

Understanding these conversions is crucial for accurate data transfer rate calculations, especially in networking and data storage where both base 10 and base 2 units are commonly used.