Mebibits per day to Gibibits per second conversion

How to convert mebibits per day to gibibits per second?

To convert 1 Mebibit per day (Mib/day) to Gibibits per second (Gib/s), we need to follow these steps:

1. Understand the Units:

   • 1 Mebibit (Mib) = $2^{20}$ bits = 1,048,576 bits (using base 2).
   • 1 Gibibit (Gib) = $2^{30}$ bits = 1,073,741,824 bits (using base 2).

   In base 10, these units are:

   • 1 Mebibit (Mib) = $10^6$ bits (1,000,000 bits).
   • 1 Gibibit (Gib) = $10^9$ bits (1,000,000,000 bits).

2. Convert Mebibits per day to Mebibits per second: There are 86,400 seconds in a day (24 hours * 60 minutes * 60 seconds).

   $\text{1 Mib/day in Mib/s} = \frac{1 \text{ Mib}}{86,400 \text{ s}}$

3. Convert Mebibits per second to Gibibits per second: Using base 2:

   $\text{1 Mib} = \frac{1}{1024} \text{ Gib} \implies \text{1 Mib/s} = \frac{1}{1024} \text{ Gib/s}$

   Thus,

   $\frac{1 \text{ Mib}}{86,400 \text{ s}} \times \frac{1 \text{ Gib}}{1024 \text{ Mib}} = \frac{1}{86,400 \times 1024} \text{ Gib/s} = \frac{1}{88,473,600} \text{ Gib/s}$

   For base 10:

   $\text{1 Mib} = \frac{10^6 \text{ bits}}{10^9 \text{ bits in 1 Gib}} = 10^{-3} \text{ Gib }$

   So,

   $\frac{1 \text{ Mib}}{86,400 \text{ s}} \times 10^{-3} \text{ Gib} = \frac{1}{86,400} \times 10^{-3} \text{ Gib/s} = \frac{10^{-3}}{86,400} \text{ Gib/s} = \frac{1}{86,400,000} \text{ Gib/s}$

In summary:

• Base 2: $\frac{1}{88,473,600}$ Gib/s.
• Base 10: $\frac{1}{86,400,000}$ Gib/s.

Real-World Examples

1. 10 Mebibits per day:

   • Base 2: $\frac{10}{88,473,600}$ Gib/s ≈ $1.13 \times 10^{-7}$ Gib/s.
   • Base 10: $\frac{10}{86,400,000}$ Gib/s ≈ $1.16 \times 10^{-7}$ Gib/s.

2. 100 Mebibits per day:

   • Base 2: $\frac{100}{88,473,600}$ Gib/s ≈ $1.13 \times 10^{-6}$ Gib/s.
   • Base 10: $\frac{100}{86,400,000}$ Gib/s ≈ $1.16 \times 10^{-6}$ Gib/s.

3. 1,000 Mebibits per day:

   • Base 2: $\frac{1,000}{88,473,600}$ Gib/s ≈ $1.13 \times 10^{-5}$ Gib/s.
   • Base 10: $\frac{1,000}{86,400,000}$ Gib/s ≈ $1.16 \times 10^{-5}$ Gib/s.

These conversions can be practical in comparing daily data usage rates to constant data transfer rates, such as when planning network capacities or analyzing data flow over time.