Bytes per second to Gibibytes per minute conversion

How to convert bytes per second to gibibytes per minute?

Converting bytes per second (B/s) to gibibytes per minute (GiB/min) involves understanding the relationship between these units:

1. Concepts and conversions:

   • Base 2 (binary - used in computing): 1 byte = 8 bits (common for both) 1 kibibyte (KiB) = 2^10 bytes = 1,024 bytes 1 mebibyte (MiB) = 2^20 bytes = 1,048,576 bytes 1 gibibyte (GiB) = 2^30 bytes = 1,073,741,824 bytes

   • Base 10 (decimal - more often used for storage devices): 1 kilobyte (KB) = 10^3 bytes = 1,000 bytes 1 megabyte (MB) = 10^6 bytes = 1,000,000 bytes 1 gigabyte (GB) = 10^9 bytes = 1,000,000,000 bytes

2. Conversions:

   • Base 2 (binary conversion):

     Start with the given rate: $1 \text{ B/s}$

     Calculate seconds in one minute: $60 \text{ seconds per minute}$

     Convert bytes per minute: $1 \text{ B/s} \times 60 \text{ seconds} = 60 \text{ B/min}$

     Convert to gibibytes per minute: $\text{GiB/min} = \frac{60 \text{ bytes}}{1,073,741,824 \text{ bytes per GiB}}$ $\text{GiB/min} \approx 5.58794 \times 10^{-8} \text{ GiB/min}$

     So, $1 \text{ B/s} \approx 5.58794 \times 10^{-8} \text{ GiB/min}$ in base 2.

   • Base 10 (decimal conversion):

     Start with the given rate: $1 \text{ B/s}$

     Calculate seconds in one minute: $60 \text{ seconds per minute}$

     Convert bytes per minute: $1 \text{ B/s} \times 60 \text{ seconds} = 60 \text{ B/min}$

     Convert to gigabytes per minute: $\text{GB/min} = \frac{60 \text{ bytes}}{1,000,000,000 \text{ bytes per GB}}$ $\text{GB/min} = 6 \times 10^{-8} \text{ GB/min}$

     So, $1 \text{ B/s} = 6 \times 10^{-8} \text{ GB/min}$ in base 10.

3. Real-world examples:

   • 10 B/s:

     • $10 \text{ B/s} \times 60 \text{ s/min} = 600 \text{ B/min}$
     • In base 2: $\approx 5.58794 \times 10^{-7} \text{ GiB/min}$
     • In base 10: $6 \times 10^{-7} \text{ GB/min}$

   • 1 KB/s (kilobyte per second):

     • $1,000 \text{ B/s} \times 60 \text{ s} = 60,000 \text{ B/min}$ // base 10
     • $1,024 \text{ B/s} \times 60 = 61,440 \text{ B/min}$ // base 2
     • In base 10: $60 \times 10^{-6} \text{ GB/min} \approx 0.00006 \text{ GB/min}$
     • In base 2: $61,440 / 1,073,741,824 \approx 5.72078 \times 10^{-5} \text{ GiB/min}$

   • 10 MB/s (megabyte per second):

     • $10,000,000 \text{ B/s} \times 60 = 600,000,000 \text{ B/min}$ // base 10
     • $10 \times 1,048,576 \text{ B/s} \times 60 = 629,145,600 \text{ B/min}$ // base 2
     • In base 10: $600,000,000 / 1,000,000,000 = 0.6 \text{ GB/min}$
     • In base 2: $629,145,600 / 1,073,741,824 \approx 0.58594 \text{ GiB/min}$

   • 100 MB/s (megabyte per second):

     • $100,000,000 \text{ B/s} \times 60 = 6,000,000,000 \text{ B/min}$ // base 10
     • $100 \times 1,048,576 \text{ B/s} \times 60 = 6,291,456,000 \text{ B/min}$ // base 2
     • In base 10: $6,000,000,000 / 1,000,000,000 = 6 \text{ GB/min}$
     • In base 2: $6,291,456,000 / 1,073,741,824 \approx 5.859375 \text{ GiB/min}$