Mebibytes per second to Mebibits per day conversion

How to convert mebibytes per second to mebibits per day?

To convert from Mebibytes per second (MiB/s) to Mebibits per day, we need to know the following:

1. The number of seconds in a day.
2. The conversion between Mebibytes and Mebibits.

Base 2 (Binary)

1. Number of seconds in a day:

   • There are $24 \times 60 \times 60 = 86,400$ seconds in a day.

2. Conversion from Mebibytes to Mebibits:

   • 1 Mebibyte (MiB) = 8 Mebibits (Mib). This is because 1 Byte = 8 bits and both Mebibytes and Mebibits use the same base (2^20 for Mebibytes and 2^20 for Mebibits).

Therefore, if you are transferring data at 1 MiB/s, we can first convert this to Mib/s and then to Mib/day.

$1 \ \text{MiB/s} = 1 \ \text{MiB/s} \times 8 \ \frac{\text{Mib}}{\text{MiB}} = 8 \ \text{Mib/s}$

Now convert this to Mib/day:

$8 \ \text{Mib/s} \times 86,400 \ \frac{\text{seconds}}{\text{day}} = 691,200 \ \text{Mib/day}$

Base 10 (Decimal)

In the decimal system, there is a slight difference because 1 Megabyte (MB) = 10^6 Bytes, and 1 Megabit (Mb) = 10^6 bits.

However, in the binary system (base 2), 1 Mebibyte (MiB) = 2^20 Bytes and 1 Mebibit (Mib) = 2^20 bits. Since both MiB and Mib use the binary base, a direct conversion in decimal terms isn't applicable. The above binary-based conversion is accurate for Mebibytes and Mebibits.

Real-World Examples:

Let's consider different data rates:

1. 10 MiB/s to Mib/day:

   $10 \ \text{MiB/s} \times 8 \ \frac{\text{Mib}}{\text{MiB}} = 80 \ \text{Mib/s}$

   $80 \ \text{Mib/s} \times 86,400 \ \frac{\text{seconds}}{\text{day}} = 6,912,000 \ \text{Mib/day}$

2. 0.5 MiB/s to Mib/day:

   $0.5 \ \text{MiB/s} \times 8 \ \frac{\text{Mib}}{\text{MiB}} = 4 \ \text{Mib/s}$

   $4 \ \text{Mib/s} \times 86,400 \ \frac{\text{seconds}}{\text{day}} = 345,600 \ \text{Mib/day}$

3. 100 MiB/s to Mib/day:

   $100 \ \text{MiB/s} \times 8 \ \frac{\text{Mib}}{\text{MiB}} = 800 \ \text{Mib/s}$

   $800 \ \text{Mib/s} \times 86,400 \ \frac{\text{seconds}}{\text{day}} = 69,120,000 \ \text{Mib/day}$

These examples illustrate how various data rates in Mebibytes per second can be converted to Mebibits per day using the base 2 binary system.