Mebibytes per hour to Gigabytes per second conversion

How to convert mebibytes per hour to gigabytes per second?

Sure! To convert 1 Mebibytes per hour (MiB/h) to Gigabytes per second (GB/s), we need to understand a few fundamental unit conversions first:

1. Base 2 (Binary) Conversions:

   • 1 Mebibyte (MiB) = 2^20 bytes = 1,048,576 bytes.
   • 1 Gigabyte (GiB) = 2^30 bytes = 1,073,741,824 bytes.
   • 1 hour = 3600 seconds.

First, convert 1 MiB to bytes: $1 \text{ MiB} = 1,048,576 \text{ bytes}$

Next, to find bytes per second, divide by the number of seconds in an hour: $\text{Bytes per second} = \frac{1,048,576 \text{ bytes}}{3600 \text{ seconds}} \approx 291.27 \text{ bytes/second}$

Then, convert bytes per second to gigabytes per second: $\text{GB per second (base 2)} = \frac{291.27 \text{ bytes/second}}{1,073,741,824 \text{ bytes/GiB}} \approx 2.71 \times 10^{-7} \text{ GiB/s}$

2. Base 10 (Decimal) Conversions:

   • 1 Megabyte (MB) = 10^6 bytes = 1,000,000 bytes.
   • 1 Gigabyte (GB) = 10^9 bytes = 1,000,000,000 bytes.
   • 1 hour = 3600 seconds.

First, convert 1 MB to bytes: $1 \text{ MB} = 1,000,000 \text{ bytes}$

Next, to find bytes per second, divide by the number of seconds in an hour: $\text{Bytes per second} = \frac{1,000,000 \text{ bytes}}{3600 \text{ seconds}} \approx 277.78 \text{ bytes/second}$

Then, convert bytes per second to gigabytes per second: $\text{GB per second (base 10)} = \frac{277.78 \text{ bytes/second}}{1,000,000,000 \text{ bytes/GB}} \approx 2.78 \times 10^{-7} \text{ GB/s}$

Real-World Examples for Other Quantities of Mebibytes per Hour

1. 10 MiB/h to GiB/s:

   • Base 2: $\frac{10 \times 1,048,576 \text{ bytes}}{3600 \text{ seconds}} \approx 2,912.7 \text{ bytes/second}$ $\frac{2,912.7 \text{ bytes/second}}{1,073,741,824 \text{ bytes/GiB}} \approx 2.71 \times 10^{-6} \text{ GiB/s}$

   • Base 10: $\frac{10 \times 1,000,000 \text{ bytes}}{3600 \text{ seconds}} \approx 2,777.8 \text{ bytes/second}$ $\frac{2,777.8 \text{ bytes/second}}{1,000,000,000 \text{ bytes/GB}} \approx 2.78 \times 10^{-6} \text{ GB/s}$

2. 100 MiB/h to GiB/s:

   • Base 2: $\frac{100 \times 1,048,576 \text{ bytes}}{3600 \text{ seconds}} \approx 29,127 \text{ bytes/second}$ $\frac{29,127 \text{ bytes/second}}{1,073,741,824 \text{ bytes/GiB}} \approx 2.71 \times 10^{-5} \text{ GiB/s}$

   • Base 10: $\frac{100 \times 1,000,000 \text{ bytes}}{3600 \text{ seconds}} \approx 27,778 \text{ bytes/second}$ $\frac{27,778 \text{ bytes/second}}{1,000,000,000 \text{ bytes/GB}} \approx 2.78 \times 10^{-5} \text{ GB/s}$

These conversions and examples illustrate the significant differences between base 2 and base 10 calculations in data transfer rates.