Bytes per second to Mebibytes per second conversion

How to convert bytes per second to mebibytes per second?

To convert 1 Byte per second (B/s) to Mebibytes per second (MiB/s), we need to understand the differences between base-10 (decimal) and base-2 (binary) measurements.

Base-10 (Decimal)

In the base-10 system which uses SI units:

• 1 Kilobyte (KB) = 10^3 Bytes = 1,000 Bytes
• 1 Megabyte (MB) = 10^6 Bytes = 1,000,000 Bytes

To convert from Bytes per second (B/s) to Megabytes per second (MB/s): $1 \text{ B/s} \times \frac{1 \text{ MB}}{10^6 \text{ Bytes}} = 1 \times 10^{-6} \text{ MB/s} = 0.000001 \text{ MB/s}$

Base-2 (Binary)

In the base-2 system which uses IEC binary units:

• 1 Kibibyte (KiB) = 2^10 Bytes = 1,024 Bytes
• 1 Mebibyte (MiB) = 2^20 Bytes = 1,048,576 Bytes

To convert from Bytes per second (B/s) to Mebibytes per second (MiB/s): $1 \text{ B/s} \times \frac{1 \text{ MiB}}{2^{20} \text{ Bytes}} = 1 \times \frac{1}{1,048,576} \text{ MiB/s} = 0.00000095367431640625 \text{ MiB/s}$

Real-World Examples

1. Internet Speed

• 1 Mbps (Megabit per second) = 1,000,000 bits per second ≈ 125,000 Bytes per second
  • Base-10: $\frac{125,000 \text{ B/s}}{10^6} = 0.125 \text{ MB/s}$
  • Base-2: $\frac{125,000 \text{ B/s}}{1,048,576} ≈ 0.119 \text{ MiB/s}$

2. USB 3.0

• 5 Gbps (Gigabit per second) = 5,000,000,000 bits per second ≈ 625,000,000 Bytes per second
  • Base-10: $\frac{625,000,000 \text{ B/s}}{10^6} = 625 \text{ MB/s}$
  • Base-2: $\frac{625,000,000 \text{ B/s}}{1,048,576} ≈ 596.046 \text{ MiB/s}$

3. SATA HDD

• 600 MBps (Megabyte per second) = 600,000,000 Bytes per second
  • Base-10: $\frac{600,000,000 \text{ B/s}}{10^6} = 600 \text{ MB/s}$
  • Base-2: $\frac{600,000,000 \text{ B/s}}{1,048,576} ≈ 572.205 \text{ MiB/s}$

Understanding these conversions helps in comparing data transfer rates across different technologies and media, as well as selecting appropriate components for desired performance levels in computing environments.