Kibibits per second to Gibibytes per second conversion

How to convert kibibits per second to gibibytes per second?

To convert from Kibibits per second (Kibps) to Gibibytes per second (GiBps), you need to understand the relationship between these units in the binary (base 2) system.

1 Kibibit (Kib) = 2^10 bits = 1024 bits 1 Mebibit (Mib) = 2^20 bits = 1,048,576 bits 1 Gibibit (Gib) = 2^30 bits = 1,073,741,824 bits

Similarly, for bytes: 1 Gibibyte (GiB) = 2^30 bytes

Conversion from Kibibits per second to Gibibytes per second (Base 2):

1. First, convert Kibibits to Gibibits.
2. Then convert Gibibits to Gibibytes.

Steps in Base 2:

1. Convert Kibibits to bits: $1 \text{ Kibps} = 1024 \text{ bits per second}$

2. Convert bits to bytes (since there are 8 bits in a byte): $\text{Bits to Bytes} = \frac{1024 \text{ bits}}{8} = 128 \text{ bytes per second}$

3. Convert bytes to Gibibytes: $\text{Bytes to GiB} = \frac{128 \text{ bytes per second}}{2^{30}}$ $= \frac{128}{1,073,741,824}$ $\approx 1.19209 \times 10^{-7} \text{ GiB per second}$

Conversion from Kibibits per second to Gigabytes per second (Base 10):

In base 10: 1 Kilobit (Kb) = 10^3 bits = 1,000 bits 1 Megabit (Mb) = 10^6 bits = 1,000,000 bits 1 Gigabit (Gb) = 10^9 bits = 1,000,000,000 bits

Gigabyte (GB) in base 10 is: 1 GB = 10^9 bytes

Steps in Base 10:

1. Convert Kibibits to bits: $1 \text{ Kibps} = 1000 \text{ bits per second}$

2. Convert bits to bytes (since there are 8 bits in a byte): $\text{Bits to Bytes} = \frac{1000 \text{ bits}}{8} = 125 \text{ bytes per second}$

3. Convert bytes to Gigabytes: $\text{Bytes to GB} = \frac{125 \text{ bytes per second}}{10^9}$ $= 1.25 \times 10^{-7} \text{ GB per second}$

Real-world Examples:

Let's consider some real-world quantities of Kibibits per second:

• 56 Kibps: Typical speed of a traditional dial-up internet connection.

  • Conversion:
    • Base 2: $56 \text{ Kibps} = 56 \times 1.19209 \times 10^{-7} \approx 6.6777 \times 10^{-6} \text{ GiBps}$
    • Base 10: $56 \text{ Kibps} = 56 \times 1.25 \times 10^{-7} = 7 \times 10^{-6} \text{ GBps}$

• 1,024 Kibps: Equivalent to 1 Mebibit per second (Mibps), which is a common speed for DSL connections.

  • Conversion:
    • Base 2: $1,024 \text{ Kibps} \approx 1.19209 \times 10^{-4} \text{ GiBps}$
    • Base 10: $1,024 \text{ Kibps} \approx 1.28 \times 10^{-4} \text{ GBps}$

• 10,240 Kibps: A lower-tier broadband connection speed.

  • Conversion:
    • Base 2: $10,240 \text{ Kibps} \approx 1.19209 \times 10^{-3} \text{ GiBps}$
    • Base 10: $10,240 \text{ Kibps} \approx 1.28 \times 10^{-3} \text{ GBps}$

In summary:

• In base 2, 1 Kibibit per second is approximately $1.19209 \times 10^{-7}$ GiBps.
• In base 10, 1 Kibibit per second is approximately $1.25 \times 10^{-7}$ GBps.

The slight differences emerge due to the different scaling factors in base 10 versus base 2.