Megabits per day to Gibibits per second conversion

How to convert megabits per day to gibibits per second?

Conversion from Megabits per Day to Gibibits per Second

To convert from megabits per day to gibibits per second, we need to understand the time conversion and the relationship between megabits and gibibits.

1. Time Conversion: There are $24$ hours in a day, $60$ minutes in an hour, and $60$ seconds in a minute. Therefore, there are: $24 \times 60 \times 60 = 86400 \text{ seconds in a day}$

2. Unit Conversion:

   • Base 10 Conversion:

     • $1 \text{ Megabit (Mb)} = 10^6 \text{ bits} = 1,000,000 \text{ bits}$
     • $1 \text{ Gibibit (Gib)} = 2^{30} \text{ bits} = 1,073,741,824 \text{ bits}$

   • Base 2 Conversion:

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

Steps to Convert

Base 10 (Decimal)

1. Convert $1 \text{ Mb}$ to bits: $1 \text{ Mb} = 1,000,000 \text{ bits}$

2. Find the number of bits per second: $\frac{1,000,000 \text{ bits}}{86400 \text{ seconds}} \approx 11.574 \text{ bits/second}$

3. Convert bits per second to Gibibits per second: $1 \text{ Gib} = 1,073,741,824 \text{ bits}$ $\frac{11.574 \text{ bits/second}}{1,073,741,824 \text{ bits}} \approx 1.078 \times 10^{-8} \text{ Gib/second}$

Base 2 (Binary)

1. Convert $1 \text{ Mib}$ to bits: $1 \text{ Mib} = 1,048,576 \text{ bits}$

2. Find the number of bits per second: $\frac{1,048,576 \text{ bits}}{86400 \text{ seconds}} \approx 12.138 \text{ bits/second}$

3. Convert bits per second to Gibibits per second: $1 \text{ Gib} = 1,073,741,824 \text{ bits}$ $\frac{12.138 \text{ bits/second}}{1,073,741,824 \text{ bits}} \approx 1.129 \times 10^{-8} \text{ Gib/second}$

Summary

• Base 10: $\approx 1.078 \times 10^{-8} \text{ Gib/second}$
• Base 2: $\approx 1.129 \times 10^{-8} \text{ Gib/second}$

Real World Examples

1. 50 Megabits per day:

   • Base 10: $50 \times 1.078 \times 10^{-8} \approx 5.39 \times 10^{-7} \text{ Gib/second}$
   • Base 2: $50 \times 1.129 \times 10^{-8} \approx 5.645 \times 10^{-7} \text{ Gib/second}$

2. 100 Megabits per day:

   • Base 10: $100 \times 1.078 \times 10^{-8} \approx 1.078 \times 10^{-6} \text{ Gib/second}$
   • Base 2: $100 \times 1.129 \times 10^{-8} \approx 1.129 \times 10^{-6} \text{ Gib/second}$

3. 500 Megabits per day:

   • Base 10: $500 \times 1.078 \times 10^{-8} \approx 5.39 \times 10^{-6} \text{ Gib/second}$
   • Base 2: $500 \times 1.129 \times 10^{-8} \approx 5.645 \times 10^{-6} \text{ Gib/second}$

These examples give you an idea of the magnitude of data transfer rates when expressed in Gibibits per second, taking into account both base 10 and base 2 calculations.