Gigabits per month to Gibibytes per month conversion

How to convert gigabits per month to gibibytes per month?

To convert 1 Gigabit per month (Gbit/month) to Gibibytes per month (GiB/month), we need to consider the differences in binary and decimal calculations.

Base 10 (Decimal)

In the decimal system, 1 Gigabit (Gbit) equals $10^9$ bits. To convert bits to bytes: $1 \text{ byte} = 8 \text{ bits}$ Therefore, in decimal: $1 \text{ Gbit} = 10^9 \text{ bits}$ $1 \text{ Gbit} = \frac{10^9 \text{ bits}}{8} \text{ bytes} = 125,000,000 \text{ bytes}$

Now, to convert bytes to gigabytes (GB) in base 10 (aware that this is not Gibibytes yet but a necessary step): $1 \text{ GB} = 10^9 \text{ bytes}$ $1 \text{ Gbit} = \frac{125,000,000 \text{ bytes}}{10^9 \text{ bytes/GB}} = 0.125 \text{ GB}$

Next, convert gigabytes to gibibytes (GiB), where: $1 \text{ GiB} = 2^{30} \text{ bytes} \approx 1.07374 \times 10^9 \text{ bytes}$ $1 \text{ GB} = 10^9 \text{ bytes}$ $1 \text{ GB} = \frac{10^9 \text{ bytes}}{2^{30} \text{ bytes/GiB}} \approx 0.931322574615478 \text{ GiB}$

So: $1 \text{ Gbit/month} = 0.125 \text{ GB/month}$ $0.125 \text{ GB/month} \times 0.931322574615478 \text{ GiB/GB} \approx 0.11641532182693475 \text{ GiB/month}$

Base 2 (Binary)

In the binary system, 1 Gigabit (Gbit) equals $2^{30}$ bits. To convert bits to bytes: $1 \text{ byte} = 8 \text{ bits}$ Therefore, in binary: $1 \text{ Gbit} = 2^{30} \text{ bits}$ $1 \text{ Gbit} = \frac{2^{30} \text{ bits}}{8} \text{ bytes} = 2^{27} \text{ bytes} \approx 134,217,728 \text{ bytes}$

Now convert bytes to gibibytes (GiB) in base 2: $1 \text{ GiB} = 2^{30} \text{ bytes}$ $1 \text{ Gbit} = \frac{2^{27} \text{ bytes}}{2^{30} \text{ bytes/GiB}} = 2^{-3} \text{ GiB} = 0.125 \text{ GiB}$

Summary

• Base 10 (decimal) calculation: 1 Gbit/month ≈ 0.1164 GiB/month
• Base 2 (binary) calculation: 1 Gbit/month = 0.125 GiB/month

Real World Examples

1. Internet Plans:

   • If an internet plan offers 50 Gbit/month of data transfer, in base 2, this is: $50 \text{ Gbit/month} \approx 50 \times 0.125 \text{ GiB/month} = 6.25 \text{ GiB/month}$ In base 10: $50 \times 0.1164 \approx 5.82 \text{ GiB/month}$

2. Data Downloads:

   • Downloading a Linux distribution of 4 GiB at a speed of 100 Gbit/month: $100 \times 0.125 \text{ GiB/month} = 12.5 \text{ GiB/month}$ So, you can download the distribution approximately 3 times in a month using the given data limits.

3. Datacenter Operations:

   • A datacenter having an upload quota of 200 Gbit/month: $200 \text{ Gbit/month} \times 0.125 \text{ GiB/month} = 25 \text{ GiB/month}$ This converts to approximately 23.28 GiB/month using base 10 calculation.

These conversions help in understanding usage limits, plan choices, and data management in various practical scenarios.