Megabytes per second to Gibibytes per day conversion

How to convert megabytes per second to gibibytes per day?

Certainly, let's go through the conversion process step-by-step for both base 10 (decimal) and base 2 (binary) notations.

Base 10 (Decimal)

1. Convert Megabytes to Bytes:

   • 1 Megabyte (MB) = 1,000,000 bytes

2. Convert Bytes per second to Bytes per day:

   • 1 MB/s = 1,000,000 bytes/second
   • There are 60 seconds in a minute, 60 minutes in an hour, and 24 hours in a day, so: $\text{Bytes per day} = 1,000,000 \, \text{bytes/sec} \times 60 \, \text{sec/min} \times 60 \, \text{min/hour} \times 24 \, \text{hours/day}$ $= 1,000,000 \times 60 \times 60 \times 24$ $= 86,400,000,000 \, \text{bytes/day}$

3. Convert Bytes to Gibibytes (GiB):

   • 1 Gibibyte (GiB) = $2^{30}$ bytes = 1,073,741,824 bytes $\text{Gibibytes per day} = \frac{86,400,000,000 \, \text{bytes}}{1,073,741,824 \, \text{bytes/GiB}}$ $\approx 80.4 \, \text{GiB/day}$

Base 2 (Binary)

1. Convert Megabytes to Mebibytes:

   • 1 Megabyte (MB) = 1,000,000 bytes
   • 1 Megabyte (MB) = ~0.953674 Mebibytes (MiB)

2. Convert Mebibytes to Bytes:

   • 1 Mebibyte (MiB) = $2^{20}$ bytes = 1,048,576 bytes
   • Therefore, 0.953674 Mebibytes = 0.953674 × 1,048,576 bytes = 999,999.94 bytes ≈ 1,000,000 bytes (as shown earlier; minor difference due to rounding)

3. Convert Bytes per second to Bytes per day:

   • Same calculation as above (since 1 MB/s ≈ 0.953674 MiB/s): $\text{Bytes per day} = 86,400,000,000 \, \text{bytes/day}$

4. Convert Bytes to Gibibytes (GiB):

   • 1 Gibibyte (GiB) = $2^{30}$ bytes = 1,073,741,824 bytes (as calculated above) $\text{Gibibytes per day} = \frac{86,400,000,000 \, \text{bytes}}{1,073,741,824 \text{bytes/GiB}}$ $\approx 80.4 \, \text{GiB/day}$

Real-World Examples Using Different Data Rates

1. 5 MB/s:

   • $5 \times 86,400,000,000 \, \text{bytes/day} = 432,000,000,000 \, \text{bytes/day}$
   • In GiB: $\approx 5 \times 80.4 \approx 402 \, \text{GiB/day}$

2. 10 MB/s:

   • $10 \times 86,400,000,000 \, \text{bytes/day} = 864,000,000,000 \, \text{bytes/day}$
   • In GiB: $\approx 10 \times 80.4 \approx 804 \, \text{GiB/day}$

3. 50 MB/s:

   • $50 \times 86,400,000,000 \, \text{bytes/day} = 4,320,000,000,000 \, \text{bytes/day}$
   • In GiB: $\approx 50 \times 80.4 \approx 4,020 \, \text{GiB/day}$

Conclusion

Regardless of the base (binary or decimal) you use, the daily conversion from Megabytes per second to Gibibytes remains approximately the same due to the closeness of the factors involved (1 MB ≈ 0.953674 MiB). For practical scenarios, especially involving large data transfers, computer science more often uses binary prefixes like Gibibytes for precise data measurements.