Megabytes per day to Mebibits per second conversion

How to convert megabytes per day to mebibits per second?

Converting 1 Megabyte per day to Mebibits per second requires a few steps, involving the conversion of bytes to bits, the understanding of the difference between decimal (base 10) and binary (base 2) prefixes, and the time conversion from days to seconds.

Conversion Steps

1. Convert Days to Seconds: One day = 24 hours = 24 * 60 minutes = 24 * 60 * 60 seconds.

   • $1 \text{ day} = 86400 \text{ seconds}$

2. Convert Megabytes to Bits:

   • Base 10 (Decimal, SI units): 1 Megabyte (MB) = $10^6$ bytes = $8 \times 10^6$ bits.
   • Base 2 (Binary, IEC units): 1 Mebibyte (MiB) = $2^{20}$ bytes = $8 \times 2^{20}$ bits.

3. Convert Bits to Mebibits:

   • Base 10: 1 Megabit (Mb) = $10^6$ bits.
   • Base 2: 1 Mebibit (Mib) = $2^{20}$ bits.

Steps for Base 10

1. Convert 1 Megabyte to bits (Base 10):

   • $1 \text{ MB} = 8 \times 10^6 \text{ bits}$.

2. Convert bits per day to bits per second:

   • $\frac{8 \times 10^6 \text{ bits}}{86400 \text{ seconds}}$.

3. Calculate bits per second:

   • $\frac{8 \times 10^6}{86400} \approx 92.5925926 \text{ bps}$.

4. Convert to Megabits per second (Base 10):

   • $\frac{92.5925926 \text{ bps}}{10^6} \approx 0.0926 \text{ Mbps}$.

5. Convert to Mebibits per second (Base 2):

   • $\frac{92.5925926 \text{ bps}}{2^{20}} \approx 0.0881 \text{ Mibps}$.

Steps for Base 2

1. Convert 1 MiB to bits:

   • $1 \text{ MiB} = 8 \times 2^{20} \text{ bits} = 8 \times 1048576 = 8388608 \text{ bits}$.

2. Convert bits per day to bits per second:

   • $\frac{8388608 \text{ bits}}{86400 \text{ seconds}} \approx 97.087 \text{ bps}$.

3. Convert to Mebibits per second:

   • $\frac{97.087 \text{ bps}}{2^{20}} \approx 0.0926 \text{ Mibps}$.

Real World Examples for Megabytes per Day

1. 10 Megabytes per day:

   • Base 10: $\approx 0.926 \text{ Mbps}$.
   • Base 2: $\approx 0.926 \text{ Mibps}$.

2. 100 Megabytes per day:

   • Base 10: $\approx 9.26 \text{ Mbps}$.
   • Base 2: $\approx 9.26 \text{ Mibps}$.

3. 1000 Megabytes per day:

   • Base 10: $\approx 92.6 \text{ Mbps}$.
   • Base 2: $\approx 92.6 \text{ Mibps}$.

4. 1 Gigabyte per day (equivalent to 1000 Megabytes per day in Base 10):

   • Base 10: $\approx 92.6 \text{ Mbps}$.
   • Base 2: (interpreting 1 GiB which is 1024 MiB): $\approx 94.17 \text{ Mibps}$.

Summary

• 1 Megabyte per day is approximately $0.0926 \text{ Mbps}$ (Base 10) or $0.0881 \text{ Mibps}$ (Base 2).
• 1 Mebibyte per day is approximately $0.0926 \text{ Mibps}$.

The difference arises due to the different interpretations of data sizes using decimal versus binary prefixes.