Gigabits per hour to Kibibits per second conversion

How to convert gigabits per hour to kibibits per second?

To convert 1 Gigabit per hour (Gbit/hr) to Kibibits per second (Kibit/s), we need to go through a series of unit conversions. Below are the steps required to convert 1 Gbit/hr to Kibit/s for both base 10 (decimal) and base 2 (binary).

Conversion Steps

1. Convert Gigabits to bits:

   • In base 10 (decimal), 1 Gigabit (Gbit) = 10^9 bits.
   • In base 2 (binary), 1 Gibibit (Gibit) = 2^30 bits (note: 1 Gbit in base 2 is actually a Gibibit).

2. Convert hours to seconds:

   • 1 hour = 3600 seconds.

3. Calculate the Data Transfer Rate in bits per second:

   • Base 10: 1 Gbit/hr = $10^9 \, \text{bits} / 3600 \, \text{seconds}$.
   • Base 2: 1 Gibit/hr = $2^{30} \, \text{bits} / 3600 \, \text{seconds}$.

4. Convert bits per second to Kibibits per second (Kibit/s):

   • In base 10, 1 Kibibit (Kibit) = 1024 bits.
   • In base 2, the conversion is similar as it is already in binary.

Detailed Calculation

Base 10 (Decimal):

1. Convert Gigabits to bits: $1 \, \text{Gbit} = 10^9 \, \text{bits}$.

2. Convert hours to seconds: $1 \, \text{hr} = 3600 \, \text{s}$.

3. Calculate bits per second: $\frac{10^9 \, \text{bits}}{3600 \, \text{s}} = 277777.78 \, \text{bits/s}$.

4. Convert to Kibibits per second: $\frac{277777.78 \, \text{bits/s}}{1024} = 271.27 \, \text{Kibit/s}$.

So, in base 10: $1 \, \text{Gbit/hr} = 271.27 \, \text{Kibit/s}$.

Base 2 (Binary):

1. Convert Gibibits to bits: $1 \, \text{Gibit} = 2^{30} \, \text{bits} = 1,073,741,824 \, \text{bits}$.

2. Convert hours to seconds: $1 \, \text{hr} = 3600 \, \text{s}$.

3. Calculate bits per second: $\frac{2^{30} \, \text{bits}}{3600 \, \text{s}} = 298,261.62 \, \text{bits/s}$.

4. Convert to Kibibits per second: $\frac{298,261.62 \, \text{bits/s}}{1024} = 291.02 \, \text{Kibit/s}$.

So, in base 2: $1 \, \text{Gibit/hr} = 291.02 \, \text{Kibit/s}$.

Real World Examples for Other Quantities of Gigabits per Hour

5 Gigabits per hour:

• Base 10: $\frac{5 \times 10^9 \, \text{bits}}{3600 \, \text{s}} \approx 1,388,888.89 \, \text{bits/s}$ $\frac{1,388,888.89 \, \text{bits/s}}{1024} \approx 1355.56 \text{ Kibit/s}$

• Base 2: $\frac{5 \times 2^{30} \, \text{bits}}{3600 \, \text{s}} \approx 1,491,308.10 \, \text{bits/s}$ $\frac{1,491,308.10 \, \text{bits/s}}{1024} \approx 1455.10 \, \text{Kibit/s}$

10 Gigabits per hour:

• Base 10: $\frac{10 \times 10^9 \, \text{bits}}{3600 \, \text{s}} \approx 2,777,777.78 \, \text{bits/s}$ $\frac{2,777,777.78 \, \text{bits/s}}{1024} \approx 2711.27 \, \text{Kibit/s}$

• Base 2: $\frac{10 \times 2^{30} \, \text{bits}}{3600 \, \text{s}} \approx 2,982,617.28 \, \text{bits/s}$ $\frac{2,982,617.28 \, \text{bits/s}}{1024} \approx 2910.20 \, \text{Kibit/s}$

These conversions allow you to understand data transfer rates in varied real world contexts, such as internet speed, data streaming, and file transfers over a network.