Bytes per second to Mebibits per second conversion

How to convert bytes per second to mebibits per second?

To convert from bytes per second (Bps) to mebibits per second (Mibps), you need to know the relationship between bytes and bits and the difference between base 10 and base 2 systems.

1 byte equals 8 bits in both systems, but the difference lies in the conversion to mebibits.

Base 10 (Decimal System)

In the base 10 (decimal) system, 1 megabit (Mb) equals 1,000,000 bits.

Steps to convert 1 Bps:

1. Convert 1 byte to bits: $1 \text{ Bps} \times 8 = 8 \text{ bits per second (bps)}$
2. Convert bits to megabits: $\frac{8 \text{ bps}}{1,000,000} = 0.000008 \text{ Mbps}$
3. Note that this is not a typical unit for measuring data rates; typically, for large quantities, you'd use kilobits, megabits, etc.

Base 2 (Binary System)

In the base 2 (binary) system, 1 mebibit (Mib) equals $2^{20}$ or 1,048,576 bits.

Steps to convert 1 Bps:

1. Convert 1 byte to bits: $1 \text{ Bps} \times 8 = 8 \text{ bits per second (bps)}$
2. Convert bits to mebibits: $\frac{8 \text{ bps}}{1,048,576} \approx 0.000007629 \text{ Mibps}$

Summary

• 1 Bps ≈ 0.000008 Mbps (base 10).
• 1 Bps ≈ 0.000007629 Mibps (base 2).

Real-World Examples

Here are some real-world examples for different quantities of Bytes per second:

• 100 Bps:

  • Base 10: $100 \times 8 / 1,000,000 = 0.0008$ Mbps
  • Base 2: $100 \times 8 / 1,048,576 = 0.0007629$ Mibps

• 1,000 Bps (1 KBps, kilobyte per second):

  • Base 10: $1,000 \times 8 / 1,000,000 = 0.008$ Mbps
  • Base 2: $1,000 \times 8 / 1,048,576 = 0.007629$ Mibps

• 1,000,000 Bps (1 MBps, megabyte per second):

  • Base 10: $1,000,000 \times 8 / 1,000,000 = 8$ Mbps
  • Base 2: $1,000,000 \times 8 / 1,048,576 \approx 7.629$ Mibps

• 10,000,000 Bps (10 MBps, megabyte per second):

  • Base 10: $10,000,000 \times 8 / 1,000,000 = 80$ Mbps
  • Base 2: $10,000,000 \times 8 / 1,048,576 \approx 76.29$ Mibps

These conversions can be helpful when comparing data transfer rates in different contexts, such as Internet speed, file transfers, and network throughput.