Mebibits per second to Gibibits per day conversion

How to convert mebibits per second to gibibits per day?

Sure, let's break down the conversion from Mebibits per second (Mib/s) to Gibibits per day (Gib/day).

Understanding Units:

1 Mebibit (Mib) = $2^{20}$ bits. 1 Gibibit (Gib) = $2^{30}$ bits.

Conversion Steps:

1. Convert 1 Mib/s to bits per second: $1 \text{ Mib/s} = 2^{20} \text{ bits/s} = 1,048,576 \text{ bits/s}$

2. Convert bits per second to bits per day: There are 86,400 seconds in a day. $1,048,576 \text{ bits/s} \times 86,400 \text{ s/day} = 90,949,017,600 \text{ bits/day}$

3. Convert bits per day to Gib/day: $\frac{90,949,017,600 \text{ bits/day}}{2^{30} \text{ bits/Gib}} = \frac{90,949,017,600 \text{ bits/day}}{1,073,741,824 \text{ bits/Gib}} \approx 84.63 \text{ Gib/day}$

So, 1 Mebibits per second is approximately 84.63 Gibibits per day.

Alternative Units (Base 10):

In the world of data transfer rates, base 10 units are often used, especially in networking equipment and manufacturers' specifications. However, Mebibits and Gibibits are already part of the base 2 system. If you were working with Megabits (Mb) and Gigabits (Gb) in base 10, you would do the calculation differently:

1 Megabit (Mb) = $10^6$ bits. 1 Gigabit (Gb) = $10^9$ bits.

For base 10 calculations:

1. Convert 1 Mb/s to bits per second: $1 \text{ Mb/s} = 1,000,000 \text{ bits/s}$

2. Convert bits per second to bits per day: $1,000,000 \text{ bits/s} \times 86,400 \text{ s/day} = 86,400,000,000 \text{ bits/day}$

3. Convert bits per day to Gb/day: $\frac{86,400,000,000 \text{ bits/day}}{10^9 \text{ bits/Gb}} = \frac{86,400,000,000 \text{ bits/day}}{1,000,000,000 \text{ bits/Gb}} = 86.4 \text{ Gb/day}$

Real-World Examples for Other Rates:

1. 10 Mebibits per second (Mib/s): Using base 2 calculation, multiply the previously found daily rate by 10. $84.63 \text{ Gib/day} \times 10 = 846.3 \text{ Gib/day}$

2. 50 Mebibits per second (Mib/s): $84.63 \text{ Gib/day} \times 50 = 4,231.5 \text{ Gib/day}$

3. 100 Mebibits per second (Mib/s): $84.63 \text{ Gib/day} \times 100 = 8,463 \text{ Gib/day}$

These conversions can be helpful for understanding the scale of data transfer, for example:

• Internet Service Providers (ISPs) might offer speeds of 100 Mib/s, which you can see would amount to approximately 8,463 Gib/day.
• Backups or large data transfers performed in a datacenter might use speeds around 1 Gib/s, which translates to roughly 84,630 Gib/day.