Kibibits per hour to Gigabits per minute conversion

How to convert kibibits per hour to gigabits per minute?

Sure, let's go through the conversion step-by-step and provide examples for both base 10 (decimal) and base 2 (binary) measures.

Understanding the Units

1 Kibibit (Kib) = 2^10 bits = 1024 bits (base 2) 1 Gigabit (Gbit) = 10^9 bits = 1,000,000,000 bits (base 10)

Conversion Formula

Base 2 (Binary)

1 Kibibit = 1024 bits 1 Gigabit = 2^30 bits = 1073741824 bits 1 hour = 60 minutes

1 Kibibit/hour to Gigabits/minute: $\text{Gigabits/minute} = \left(\frac{1 \, \text{Kib}}{1 \, \text{hour}}\right) \times \left(\frac{1024 \, \text{bits}}{2^{30} \, \text{bits/Gb}}\right) \times \left(\frac{1}{60 \, \text{minutes}}\right)$

$\text{Gigabits/minute} = \left(\frac{1024}{1073741824}\right) \times \left(\frac{1}{60}\right)$

$\text{Gigabits/minute} = \left(\frac{1024}{1073741824}\right) / 60$

$\text{Gigabits/minute} \approx \left(\frac{1024}{1073741824 \times 60}\right)$

$\text{Gigabits/minute} \approx 1.586 \times 10^{-7} \, \text{Gigabits/minute}$

Base 10 (Decimal)

1 Kibibit = 1024 bits (because we are assuming the source unit is base 2 as Kibibit) 1 Gigabit = 10^9 bits 1 hour = 60 minutes

1 Kibibit/hour to Gigabits/minute: $\text{Gigabits/minute} = \left(\frac{1 \, \text{Kib}}{1 \, \text{hour}}\right) \times \left(\frac{1024 \, \text{bits}}{10^9 \, \text{bits/Gb}}\right) \times \left(\frac{1}{60 \, \text{minutes}}\right)$

$\text{Gigabits/minute} = \left(\frac{1024}{1000000000}\right) \times \left(\frac{1}{60}\right)$

$\text{Gigabits/minute} = \left(\frac{1024}{60000000000}\right)$

$\text{Gigabits/minute} \approx 1.707 \times 10^{-8} \, \text{Gigabits/minute}$

Real-World Examples

1. Slow Data Transfer Rate Device: A small, specialized sensor collects 30 Kibibits of data per hour. How much is that in base 2 and base 10 Gigabits/minute?

   • Base 2: $\text{Gib/min} = 30 \times 1.586 \times 10^{-7}$ $\text{Gib/min} \approx 4.758 \times 10^{-6}$

   • Base 10: $\text{Gb/min} = 30 \times 1.707 \times 10^{-8}$ $\text{Gb/min} \approx 5.121 \times 10^{-7}$

2. Medium Transfer Rate Device: A weather station transmits 1 MiB (8192 Kibibits) of data every day. Converting this in an hourly data rate gives:

   • Base 2: $\text{Gib/min} = \left(\frac{8192 \, \text{Kib}}{24 \times 60}\right) \times 1.586 \times 10^{-7}$ $\text{Gib/min} \approx 9.074 \times 10^{-4}$

   • Base 10: $\text{Gb/min} = \left(\frac{8192 \, \text{Kib}}{24 \times 60}\right) \times 1.707 \times 10^{-8}$ $\text{Gb/min} \approx 9.733 \times 10^{-5}$

These examples illustrate different scenarios of Kibibits per hour converted into Gigabits per minute using both bases of calculation.