Kilobits per hour to Gibibits per hour conversion

How to convert kilobits per hour to gibibits per hour?

To convert kilobits per hour (kb/hr) to gibibits per hour (Gib/hr), you need to understand the difference between the prefixes "kilo" and "gibi" and whether you're using base 10 or base 2.

Base 10 Conversion

In base 10:

• 1 kilobit (kb) = 1,000 bits
• 1 gigabit (Gb) = 1,000,000,000 bits

Therefore, to convert kilobits to gigabits in base 10:

• 1 kilobit = 0.000001 gigabits (because 1,000 bits / 1,000,000,000 bits = 0.000001)

Since we're converting to gibibits (base 2), we need to be careful. Gibibits are different:

Base 2 Conversion

In base 2:

• 1 kilobit (kb) = 1,024 bits (2^10)
• 1 gibibit (Gib) = 1,073,741,824 bits (2^30)

Therefore, to convert kilobits to gibibits in base 2:

• 1 kilobit = $\frac{1,024 \text{ bits}}{1,073,741,824 \text{ bits}}$

Thus, $1 \text{ kb/hr} = \frac{1,024}{1,073,741,824} \text{ Gib/hr}$ $1 \text{ kb/hr} ≈ 9.5367432 \times 10^{-7} \text{ Gib/hr}$

Base 10 to Base 2 Conversion Example

Let's repeat the calculation for understanding from base 10 kilobits:

• Converting 1 kilobit (1,000 bits) to bits per second (since base 10 kilobit is 1,000 bits):
  • 1 kb/hr = 1,000 bits/hr

Now converting bits to gibibits:

• 1 gibibit = 1,073,741,824 bits
  • $1,000 \text{ bits/hr} \div 1,073,741,824 = 9.3132257 \times 10^{-7} \text{ Gib/hr}$

Real-World Examples

Here are some real-world examples involving kilobits per hour:

1. Standard Email Without Attachments:

   • Average size: 20 kilobits (kb)
   • If 1 email is sent per hour, the data transfer rate is 20 kb/hr.
   • Converted to gibibits per hour (Gi/hr): ≈ 1.9073486 \times 10^{-5} Gib/hr

2. Streaming Low-Quality Audio:

   • Average bitrate: 96 kilobits per second (kbps)
   • In an hour, this is 96 * 3,600 = 345,600 kb/hr.
   • Converted to Gib/hr: ≈ 0.3295898 Gib/hr

3. Downloading a Small Software Update:

   • File size: 10 megabytes (MB)
   • Converting MB to kilobits (1 MB = 8,000 kilobits)
   • 10 MB = 80,000 kilobits
   • If it takes 1 hour to download, this translates to 80,000 kb/hr.
   • Converted to Gib/hr: ≈ 0.0745 Gib/hr

These calculations should help illustrate how to convert kilobits per hour to gibibits per hour and provide some practical context for various data transfer scenarios.