Kibibits per hour to Gigabytes per second conversion

How to convert kibibits per hour to gigabytes per second?

To convert Kibibits per hour (Kibit/h) to Gigabytes per second (GB/s), you need to know the conversion factors between these units, which differ in base 10 (decimal) and base 2 (binary). Let's perform the conversions for both bases.

Base 2 Conversion

1 Kibibit (Kibit) = 2^10 bits = 1024 bits
1 Gigabyte (GiB) = 2^30 bytes

To go from Kibibits to bits: 1 Kibit = 1024 bits

Since there are 8 bits in a byte: 1 Gibibyte (GiB) * 8 * 2^30 bits/byte = 8 * 2^30 bits = 8,589,934,592 bits

1 hour = 3600 seconds

So, converting 1 Kibit/h to GiB/s: $1 \, \text{Kibit/h} = \frac{1024 \, \text{bits}}{3600 \, \text{seconds}}$

$1 \, \text{Kibit/h} = \frac{1024}{3600} \, \text{bits/second} = \frac{1024}{3600} \, \text{bits/s}$

We now convert bits per second to Gibibytes per second: $1 \, \text{Gibibytes} = 8,589,934,592 \, \text{bits}$

$\text{Gibibytes per second} = \frac{1024 / 3600}{8 \cdot 2^{30}} = \frac{1024}{3600 \cdot 8 \cdot 2^{30}}$ $1 \, \text{Kibit/h} \approx 3.2 \times 10^{-10} \, \text{GiB/s}$

Base 10 Conversion

1 Kibibit (Kibit) = 1024 bits (same as base 2) 1 Gigabyte (GB) = 10^9 (1,000,000,000) bytes

Similarly, converting 1 Kibit/h to bits per second: $1 \, \text{Kibit/h} = \frac{1024 \, \text{bits}}{3600 \, \text{seconds}}$

$1 \, \text{Kibit/h} = \frac{1024}{3600} \, \text{bits/s}$

Now, converting bits per second to Gigabytes per second: $1 \, \text{Gigabytes} = 8 \times 10^9 \, \text{bits}$

$\text{Gigabytes per second} = \frac{1024 / 3600}{8 \cdot 10^9} = \frac{1024}{3600 \cdot 8 \cdot 10^9}$ $1 \, \text{Kibit/h} \approx 3.6 \times 10^{-11} \, \text{GB/s}$

Summary

• Base 2: 1 Kibibit per hour ≈ 3.2 × 10^-10 GiB/s
• Base 10: 1 Kibibit per hour ≈ 3.6 × 10^-11 GB/s

Real-World Examples of Different Quantities of Kibibits per Hour

1. Streaming a standard definition video (SD): Typical data rate for SD video: ~1 Mib/s (Megabits per second, base 2) Converting to Kibibits per hour: $1 \, \text{Mib/s} = 1024 \, \text{Kibit/s}$ $\, \text{per hour} = 1024 \times 3600 = 3,686,400 \, \text{Kibit/h}$

2. Downloading a 1 GB file over a slow connection: Assume a connection speed of 56 Kib/s (Kibibits per second): $56 \, \text{Kibit/s}$ $\text{per hour} = 56 \times 3600 = 201,600 \, \text{Kibit/h}$

3. High-speed internet data consumption: Assume a high-speed internet connection of 100 Mib/s: $100 \, \text{Mib/s} = 100 \times 1024 \, \text{Kibit/s} = 102,400 \, \text{Kibit/s}$ $\text{per hour} = 102,400 \times 3600 = 368,640,000 \, \text{Kibit/h}$

These examples help illustrate the conversion process and provide context for the data transfer rates seen in everyday scenarios.