Kibibytes per second to Gigabits per second conversion

How to convert kibibytes per second to gigabits per second?

To convert Kibibytes per second (KiB/s) to Gigabits per second (Gbps), we need to understand the conversion factors between these units.

Base 2 (Binary)

In the binary system:

• 1 Kibibyte (KiB) = 2^10 Bytes = 1,024 Bytes
• 1 Byte = 8 bits
• 1 Gibibit (Gib) = 2^30 bits = 1,073,741,824 bits
• 1 Gigabit (Gb) = 2^30 / 8 = 134,217,728 bytes

So to convert KiB/s to Gbps in base 2:

1. Convert KiB to Bits: $1 \text{ KiB} = 1,024 \text{ Bytes} \times 8 \text{ bits/Byte} = 8,192 \text{ bits}$

2. Convert Bits to Gbps: $8,192 \text{ bits} / (1,073,741,824) \text{ bits/Gb} = 7.6294 \times 10^{-6} \text{ Gbps}$

Base 10 (Decimal)

In the decimal system:

• 1 Kilobyte (KB) = 10^3 Bytes = 1,000 Bytes
• 1 Byte = 8 bits
• 1 Gigabit (Gb) = 10^9 bits

So to convert KiB/s to Gbps in base 10:

1. Convert KiB to Bytes: $1 \text{ KiB} = 1,024 \text{ Bytes}$

2. Convert Bytes to Bits: $1,024 \text{ Bytes} \times 8 \text{ bits/Byte} = 8,192 \text{ bits}$

3. Convert Bits to Gbps: $8,192 \text{ bits} / 10^9 \text{ bits/Gb} = 8.192 \times 10^{-6} \text{ Gbps}$

Real-World Examples

1. 10 KiB/s:

   • Base 2: $10 \times 7.6294 \times 10^{-6} = 7.6294 \times 10^{-5} \text{ Gbps}$
   • Base 10: $10 \times 8.192 \times 10^{-6} = 8.192 \times 10^{-5} \text{ Gbps}$

2. 1 MiB/s (1024 KiB/s):

   • Base 2: $1024 \times 7.6294 \times 10^{-6} = 7.8239 \times 10^{-3} \text{ Gbps}$
   • Base 10: $1024 \times 8.192 \times 10^{-6} = 8.3886 \times 10^{-3} \text{ Gbps}$

3. 100 KiB/s:

   • Base 2: $100 \times 7.6294 \times 10^{-6} = 7.6294 \times 10^{-4} \text{ Gbps}$
   • Base 10: $100 \times 8.192 \times 10^{-6} = 8.192 \times 10^{-4} \text{ Gbps}$

These examples illustrate the conversions for different quantities of Kibibytes per second. The difference between base 2 and base 10 is relatively small but can be significant in certain contexts, especially for high-speed data transfers.