Gigabits per second to Tebibytes per second conversion

How to convert gigabits per second to tebibytes per second?

To convert from Gigabits per second (Gbps) to Tebibytes per second (TiBps), it's important to understand the distinctions between base 10 (decimal) and base 2 (binary) units.

Base 10 Conversion:

In base 10:

• 1 Gigabit (Gb) = 10^9 bits
• 1 Terabyte (TB) = 10^12 bytes = 8 * 10^12 bits (since 1 byte = 8 bits)

So to convert 1 Gbps to TBps: $1\text{ Gbps} = 10^9 \text{ bits per second}$

$\text{To convert bits to terabytes:}$ $10^9 \text{ bits per second} * \frac{1 \text{ TB}}{8 \times 10^{12} \text{ bits}} = \frac{10^9}{8 \times 10^{12}} \text{ TBps}$

$= 1.25 \times 10^{-4} \text{ TBps}$ or $= 0.000125 \text{ TBps}$

Base 2 Conversion:

In base 2:

• 1 Gibibit (Gib) = 2^30 bits
• 1 Tebibyte (TiB) = 2^40 bytes = 8 * 2^40 bits (since 1 byte = 8 bits)

So to convert 1 Gbps to TiBps: 1 Gbps is equal to 10^9 bits per second. We’ll convert bits to Tebibytes (binary terabytes) where: $1 \text{ TiB} = 2^{40} \text{ bytes}$ $1 \text{ byte} = 8 \text{ bits}$ $1 \text{ TiB} = 8 \times 2^{40} \text{ bits} = 8 \times 1,099,511,627,776 \text{ bits} = 8,796,093,022,208 \text{ bits}$

So, $10^9 \text{ bits per second}$ $= 10^9 \text{ bits per second} \div 8,796,093,022,208 \text{ bits per Tebibyte} = 1.136 \times 10^{-10} \text{ TiBps}$

Summary:

• In base 10: $1 \text{ Gbps} = 0.000125 \text{ TBps}$

• In base 2: $1 \text{ Gbps} = 1.136 \times 10^{-10} \text{ TiBps}$

Real-World Examples:

• 10 Gbps Ethernet:

  • Provides a data rate of 10 Gigabits per second
  • In base 10: 10 Gbps = 0.00125 TBps
  • In base 2: 10 Gbps = 1.136 × 10^-9 TiBps

• 100 Gbps Ethernet:

  • Provides a data rate of 100 Gigabits per second
  • In base 10: 100 Gbps = 0.0125 TBps
  • In base 2: 100 Gbps = 1.136 × 10^-8 TiBps

• Fiber Optic Internet:

  • Some state-of-the-art fiber optic services offer speeds up to 1 Gbps
  • In base 10: 1 Gbps = 0.000125 TBps
  • In base 2: 1 Gbps = 1.136 × 10^-10 TiBps

Each of these examples shows the varying scales of data transfer rates and underscores the differences between using base 10 and base 2 units.