Megabits per day to Mebibytes per second conversion

How to convert megabits per day to mebibytes per second?

To convert 1 Megabit per day (Mb/day) to Mebibytes per second (MiB/s), you need to follow a series of conversion steps.

Conversion Outline

1. Convert days to seconds: There are 86400 seconds in a day.
2. Convert Megabits to bits: 1 Megabit (Mb) = 1,000,000 bits (for base 10) or 2^20 = 1,048,576 bits (for base 2).
3. Convert bits to bytes: 1 byte = 8 bits.
4. Convert bytes to Mebibytes: 1 Mebibyte (MiB) = 2^20 bytes (base 2).

Base 10 (Decimal) Conversion

1. Convert days to seconds: $1 \text{ day} = 86400 \text{ seconds}$

2. Convert Megabits to bits: $1 \text{ Megabit} = 1,000,000 \text{ bits}$

3. Convert bits to bytes: $1,000,000 \text{ bits} = \frac{1,000,000}{8} \text{ bytes} = 125,000 \text{ bytes}$

4. Convert bytes to Mebibytes: $1 \text{ MiB} = 2^{20} \text{ bytes} = 1,048,576 \text{ bytes}$

   So, $125,000 \text{ bytes} = \frac{125,000}{1,048,576} \text{ MiB} \approx 0.1192 \text{ MiB}$

5. Megabits per day to Mebibytes per second: $\frac{0.1192 \text{ MiB}}{86400 \text{ seconds}} \approx 1.38 \times 10^{-6} \text{ MiB/s}$

Base 2 (Binary) Conversion

1. Convert days to seconds: $1 \text{ day} = 86400 \text{ seconds}$

2. Convert Megabits to bits: $1 \text{ Megabit} = 1,048,576 \text{ bits}$

3. Convert bits to bytes: $1,048,576 \text{ bits} = \frac{1,048,576}{8} \text{ bytes} = 131,072 \text{ bytes}$

4. Convert bytes to Mebibytes: $131,072 \text{ bytes} = \frac{131,072}{1,048,576} \text{ MiB} = 0.125 \text{ MiB}$

5. Megabits per day to Mebibytes per second: $\frac{0.125 \text{ MiB}}{86400 \text{ seconds}} \approx 1.45 \times 10^{-6} \text{ MiB/s}$

Real World Examples

Let’s consider some real-world examples with other quantities of Megabits per day:

1. 100 Megabits per day:

   • Base 10: $100 \text{ Mb/day} = 100 \times 1.38 \times 10^{-6} \text{ MiB/s} \approx 1.38 \times 10^{-4} \text{ MiB/s}$
   • Base 2: $100 \text{ Mb/day} = 100 \times 1.45 \times 10^{-6} \text{ MiB/s} \approx 1.45 \times 10^{-4} \text{ MiB/s}$

2. 1 Gigabit per day (1000 Mb/day):

   • Base 10: $1000 \text{ Mb/day} = 1000 \times 1.38 \times 10^{-6} \text{ MiB/s} \approx 1.38 \times 10^{-3} \text{ MiB/s}$
   • Base 2: $1000 \text{ Mb/day} = 1000 \times 1.45 \times 10^{-6} \text{ MiB/s} \approx 1.45 \times 10^{-3} \text{ MiB/s}$

3. 1 Terabit per day (1,000,000 Mb/day):

   • Base 10: $1,000,000 \text{ Mb/day} = 1,000,000 \times 1.38 \times 10^{-6} \text{ MiB/s} \approx 1.38 \text{ MiB/s}$
   • Base 2: $1,000,000 \text{ Mb/day} = 1,000,000 \times 1.45 \times 10^{-6} \text{ MiB/s} \approx 1.45 \text{ MiB/s}$

These conversions and examples illustrate the relationship between data transfer rates in different units and highlight how the base of the unit (base 10 vs. base 2) affects the calculations.