Gigabits per minute to Gibibytes per month conversion

How to convert gigabits per minute to gibibytes per month?

To convert 1 gigabit per minute (Gb/min) to gibibytes per month (GiB/month), you need to follow these steps, keeping in mind the distinction between base 10 and base 2.

Conversion Factors

1. Base 10 (Decimal System):

   • 1 gigabit (Gb) = 1,000,000,000 bits = 10^9 bits
   • 1 byte = 8 bits
   • 1 gigabyte (GB) = 10^9 bytes
   • 1 minute = 60 seconds
   • 1 hour = 60 minutes
   • 1 day = 24 hours
   • 1 month = 30 days (assuming a 30-day month for simplicity)

2. Base 2 (Binary System):

   • 1 gibibit (Gib) = 2^30 bits = 1,073,741,824 bits
   • 1 byte = 8 bits
   • 1 gibibyte (GiB) = 2^30 bytes
   • Other time conversions remain the same.

Base 10 Conversion

1. Convert gigabits to gigabytes: $\frac{1 \, \text{Gb}}{8} = 0.125 \, \text{GB}$

2. Compute the monthly data transfer:

   • 1 minute = 0.125 GB
   • 1 hour = 0.125 GB * 60 minutes = 7.5 GB
   • 1 day = 7.5 GB * 24 hours = 180 GB
   • 1 month (30 days) = 180 GB * 30 = 5,400 GB

3. Convert gigabytes to gibibytes:

   • 1 GB = 10^9 bytes
   • 1 GiB = 2^30 bytes
   • $\text{5,400 GB} = \frac{5,400 * 10^9 \text{ bytes}}{2^30 \text{ bytes/GiB}} \approx 5,021.57 \, \text{GiB}$

Base 2 Conversion

1. Convert gigabits to gibibytes:

   • 1 gigabit (Gb) = 10^9 bits; 1 Gib = 2^30 bits
   • Number of bytes in 1 minute: $\frac{1 \, \text{Gb}}{8} = \frac{10^9}{8} \, \text{bytes} \approx 125,000,000 \, \text{bytes} = 10^8 \, \text{bytes}$
   • Convert bytes to GiB: $\frac{125,000,000 \, \text{bytes}}{2^{30} \, \text{bytes/GiB}} \approx 0.116 \, \text{GiB}$

2. Compute the monthly data transfer:

   • 1 minute = 0.116 GiB
   • 1 hour = 0.116 GiB * 60 minutes = 6.96 GiB
   • 1 day = 6.96 GiB * 24 hours = 167.04 GiB
   • 1 month (30 days) = 167.04 GiB * 30 days ≈ 5,011.2 GiB

Summary

• Base 10: 1 Gigabit per minute ≈ 5,021.57 GiB per month
• Base 2: 1 Gigabit per minute ≈ 5,011.2 GiB per month

Real-World Examples

1. 10 Gigabits per minute:

   • Base 10: 10 * 5,021.57 GiB/month ≈ 50,215.7 GiB/month
   • Base 2: 10 * 5,011.2 GiB/month ≈ 50,112 GiB/month

2. 100 Megabits per minute (0.1 Gigabits):

   • Base 10: 0.1 * 5,021.57 GiB/month ≈ 502.16 GiB/month
   • Base 2: 0.1 * 5,011.2 GiB/month ≈ 501.12 GiB/month

3. 5 Gigabits per minute:

   • Base 10: 5 * 5,021.57 GiB/month ≈ 25,107.85 GiB/month
   • Base 2: 5 * 5,011.2 GiB/month ≈ 25,056 GiB/month

These examples clarify how to approach conversions between data transfer rates and monthly data volumes, considering both decimal and binary measurement systems.