Gigabits per second to Gibibytes per second conversion

How to convert gigabits per second to gibibytes per second?

To convert 1 Gigabit per second (Gbps) to Gibibytes per second (GiBps), you will need to use the appropriate conversion factors. The difference between the answers for base 10 (decimal) and base 2 (binary) is outlined below:

Base 10 (Decimal) Conversion:

In decimal, 1 Gigabit (Gb) is defined as $10^9$ (1,000,000,000) bits.

1. Convert Gigabits to bits: $1 \text{ Gbps} = 1 \times 10^9 \text{ bits per second}$

2. Convert bits to bytes (1 byte = 8 bits): $1 \text{ Gbps} = \frac{10^9 \text{ bits}}{8} = 1.25 \times 10^8 \text{ bytes per second}$

3. Convert bytes to Gigabytes (GB) where 1 GB = $10^9$ bytes: $1.25 \times 10^8 \text{ bytes per second} = \frac{1.25 \times 10^8 \text{ bytes}}{10^9} = 0.125 \text{ Gigabytes per second}$

4. Convert Gigabytes (GB) to Gibibytes (GiB) where 1 GiB = $2^{30}$ bytes: $0.125 \text{ GBps} = \frac{0.125 \times 10^9 \text{ bytes}}{2^{30} \text{ bytes per GiB}}$

   Simplify the above: $0.125 \times \frac{10^9}{2^{30}} = 0.125 \times \frac{10^9}{1,073,741,824} \approx 0.1164 \text{ GiBps}$

Base 2 (Binary) Conversion:

In binary, 1 Gibibit (Gib) is defined as $2^{30}$ bits.

1. Convert 1 Gigabit per second (Gbps) to bits: $1 \text{ Gbps} = 1 \times 10^9 \text{ bits per second}$

2. Convert bits to bytes: $1 \text{ Gbps} = \frac{10^9}{8} = 1.25 \times 10^8 \text{ bytes per second}$

3. Convert bytes to Gibibytes (GiB): $1.25 \times 10^8 \text{ bytes per second} = \frac{1.25 \times 10^8 \text{ bytes}}{2^{30} \text{ bytes per GiB}}$

   Simplify the above: $1.25 \times \frac{10^8}{2^{30}} = 1.25 \times \frac{10^8}{1,073,741,824} \approx 0.1164 \text{ GiBps}$

Summary:

• Base 10 (Decimal) conversion: $1 \text{ Gbps} ≈ 0.1164 \text{ GiBps}$
• Base 2 (Binary) conversion: $1 \text{ Gbps} ≈ 0.1164 \text{ GiBps}$

Both conversions in this case yield the same result because the computations end up being the same when translated through intermediate units. However, the processes show the importance of understanding different bases when working with units.

Real-World Examples:

• 10 Gbps Fiber Internet:
  • A service offered by ISPs that is capable of delivering 1.164 GiBps.
• 1 Gbps Ethernet Network:
  • Common in modern local area networks (LANs), translating to roughly 0.1164 GiBps.
• USB 3.1 (Gen 2) Ports:
  • These operate at up to 10 Gbps, delivering speeds up to 1.164 GiBps.
• 4K Streaming Services:
  • Streaming a 4K video might require around 25 Mbps, which is 0.025 Gbps, translating roughly to 0.00291 GiBps.