Kibibytes per second to Gigabytes per second conversion

How to convert kibibytes per second to gigabytes per second?

Converting from Kibibytes per second (KiBps) to Gigabytes per second (GBps) involves understanding the difference between base 2 (binary) and base 10 (decimal) systems. We'll perform both conversions below:

Base 2 (Binary) Conversion

In the binary system (base 2), the following relationships hold:

• 1 Kibibyte (KiB) = 2^10 bytes = 1,024 bytes
• 1 Mebibyte (MiB) = 2^10 KiB = 1,024 KiB
• 1 Gibibyte (GiB) = 2^10 MiB = 1,024 MiB
• 1 Tebibyte (TiB) = 2^10 GiB = 1,024 GiB, and so on.

Thus,

• 1 Gibibyte = 1,024^3 bytes = 1,073,741,824 bytes

To convert 1 KiBps to GiBps:

1. Convert 1 KiB to bytes: 1 KiB = 1,024 bytes

2. Convert bytes per second to GiB per second by dividing by 1,073,741,824 ( = 1,024^3):

   $1 \text{ KiBps} = \frac{1,024 \text{ bytes/sec}}{1,073,741,824 \text{ bytes}} = 9.5367431640625 \times 10^{-7} \text{ GiBps}$

Base 10 (Decimal) Conversion

In the decimal system (base 10), the following relationships hold:

• 1 Kilobyte (KB) = 10^3 bytes = 1,000 bytes
• 1 Megabyte (MB) = 10^3 KB = 1,000 KB
• 1 Gigabyte (GB) = 10^3 MB = 1,000 MB

Thus,

• 1 Gigabyte = 1,000^3 bytes = 1,000,000,000 bytes

To convert 1 KiBps to GBps:

1. Convert 1 KiB to bytes: 1 KiB = 1,024 bytes

2. Convert bytes per second to GB per second by dividing by 1,000,000,000 ( = 1,000^3):

   $1 \text{ KiBps} = \frac{1,024 \text{ bytes/sec}}{1,000,000,000 \text{ bytes}} = 1.024 \times 10^{-6} \text{ GBps}$

Real-World Examples for Different Quantities of Kibibytes per Second

1. 10 KiBps

   • In GiBps (base 2): $10 \times 9.5367431640625 \times 10^{-7} \text{ GiBps} = 9.5367431640625 \times 10^{-6} \text{ GiBps}$
   • In GBps (base 10): $10 \times 1.024 \times 10^{-6} \text{ GBps} = 1.024 \times 10^{-5} \text{ GBps}$

2. 100 KiBps

   • In GiBps (base 2): $100 \times 9.5367431640625 \times 10^{-7} \text{ GiBps} = 9.5367431640625 \times 10^{-5} \text{ GiBps}$
   • In GBps (base 10): $100 \times 1.024 \times 10^{-6} \text{ GBps} = 1.024 \times 10^{-4} \text{ GBps}$

3. 1,000 KiBps (1 MiBps)

   • In GiBps (base 2): $1,000 \times 9.5367431640625 \times 10^{-7} \text{ GiBps} = 9.5367431640625 \times 10^{-4} \text{ GiBps}$
   • In GBps (base 10): $1,000 \times 1.024 \times 10^{-6} \text{ GBps} = 1.024 \times 10^{-3} \text{ GBps}$

4. 10,000 KiBps (10 MiBps)

   • In GiBps (base 2): $10,000 \times 9.5367431640625 \times 10^{-7} \text{ GiBps} = 9.5367431640625 \times 10^{-3} \text{ GiBps}$
   • In GBps (base 10): $10,000 \times 1.024 \times 10^{-6} \text{ GBps} = 1.024 \times 10^{-2} \text{ GBps}$

These conversions help you understand the data transfer rates in different scales, making it easier to compare and communicate bandwidth requirements in both base 2 and base 10 contexts.