Gigabytes per second to bits per second conversion

How to convert gigabytes per second to bits per second?

Sure, let's break down how to convert Gigabytes per second (GBps) to bits per second (bps) using both base 10 and base 2.

Base 10 (Decimal)

In base 10, the prefix Giga- means $10^9$.

1. Conversion from Gigabytes per second to Gigabits per second (Gbps): $1 \, \text{GBps} = 1 \times 10^9 \, \text{bytes per second}$

2. Conversion from bytes to bits: Since there are 8 bits in a byte: $1 \, \text{byte} = 8 \, \text{bits}$ $1 \, \text{GBps} = 1 \times 10^9 \, \text{bytes per second} \times 8 \, \frac{\text{bits}}{\text{byte}}$

So, $1 \, \text{GBps} = 8 \times 10^9 \, \text{bps}$

Therefore, 1 GBps = 8 Gbps or $8 \times 10^9$ bits per second in base 10.

Base 2 (Binary)

In base 2, the prefix Gibi- (Gi) means $2^{30}$.

1. Conversion from Gibibytes per second to Gibibits per second: $1 \, \text{GiBps} = 2^{30} \, \text{bytes per second}$

2. Conversion from bytes to bits: Since there are 8 bits in a byte: $1 \, \text{byte} = 8 \, \text{bits}$ $1 \, \text{GiBps} = 2^{30} \, \text{bytes per second} \times 8 \, \frac{\text{bits}}{\text{byte}}$

So, $1 \, \text{GiBps} = 8 \times 2^{30} \, \text{bps}$

Therefore, $1 \, \text{GiBps} = 8 \times 2^{30} = 8 \times 1,073,741,824 = 8,589,934,592 \, \text{bps}$

Real-world Examples for Various Quantities of GBps

1. 0.5 GBps (Base 10):

   • In bits per second: $0.5 \times 8 \times 10^9 = 4 \times 10^9 \, \text{bps} = 4 \, \text{Gbps}$
   • Real-world Example: A high-speed consumer internet connection like Google Fiber, which offers plans up to 1 or 2 Gbps, is roughly in this range.

2. 2 GBps (Base 10):

   • In bits per second: $2 \times 8 \times 10^9 = 16 \times 10^9 \, \text{bps} = 16 \, \text{Gbps}$
   • Real-world Example: The internal network of large data centers, which often use multi-terabit Ethernet links.

3. 10 GBps (Base 10):

   • In bits per second: $10 \times 8 \times 10^9 = 80 \times 10^9 \, \text{bps} = 80 \, \text{Gbps}$
   • Real-world Example: High-performance computing clusters and scientific research facilities that process large datasets, such as those found in climate modeling or genomics.

4. 100 GBps (Base 10):

   • In bits per second: $100 \times 8 \times 10^9 = 800 \times 10^9 \, \text{bps} = 800 \, \text{Gbps}$
   • Real-world Example: Cutting-edge backbone networks of major internet service providers, which use technologies such as 100 Gigabit Ethernet.

Summary

For base 10 (decimal), 1 Gigabyte per second (GBps) equals 8 billion bits per second (8 Gbps). For base 2 (binary), 1 Gibibyte per second (GiBps) equals approximately 8.59 billion bits per second (8,589,934,592 bps).