Gigabytes per second to Kilobits per hour conversion

How to convert gigabytes per second to kilobits per hour?

Sure, let's break down the conversion steps and provide real-world examples for different quantities of Gigabytes per second (GBps).

Step-by-Step Conversion

1 Gigabyte per second (GBps) needs to be converted to Kilobits per hour (Kbps). To do this, we will use the following units of measurement:

• 1 Byte (B) = 8 bits (b)
• 1 Gigabyte (GB) = $10^9$ Bytes (for base 10) or $2^{30}$ Bytes (for base 2)
• 1 Kilobit (Kb) = $10^3$ bits (for base 10) or $2^{10}$ bits (for base 2)
• 1 hour = 3600 seconds

Conversion in Base 10

1. Convert GBps to bits per second (bps): $1 \, \text{GBps} \times 10^9 \, \text{Bytes} = 10^9 \, \text{Bytes per second}$ $1 \, \text{Byte} = 8 \, \text{bits}$ $10^9 \, \text{Bytes per second} \times 8 \, \text{bits per Byte} = 8 \times 10^9 \, \text{bps}$

2. Convert bps to Kilobits per second (Kbps): $8 \times 10^9 \, \text{bps} \div 10^3 = 8 \times 10^6 \, \text{Kbps}$

3. Convert Kilobits per second to Kilobits per hour: $8 \times 10^6 \, \text{Kbps} \times 3600 \, \text{seconds per hour} = 28.8 \times 10^9 \, \text{Kb/hour}$

Thus, in base 10: $1 \, \text{GBps} = 28.8 \times 10^9 \, \text{Kb/hour}$

Conversion in Base 2

1. Convert GBps to bits per second (bps): $1 \, \text{GBps} \times 2^{30} \, \text{Bytes} = 2^{30} \, \text{Bytes per second}$ $1 \, \text{Byte} = 8 \, \text{bits}$ $2^{30} \, \text{Bytes per second} \times 8 \, \text{bits per Byte} = 2^{33} \, \text{bps}$

2. Convert bps to Kilobits per second (Kbps): $2^{33} \, \text{bps} \div 2^{10} = 2^{23} \, \text{Kbps}$

3. Convert Kilobits per second to Kilobits per hour: $2^{23} \, \text{Kbps} \times 3600 \, \text{seconds per hour} = 2^{23} \times 3600 \, \text{Kb/hour} = 30 \times 2^{23} \, \text{Kb/hour}$

Thus, in base 2: $1 \, \text{GBps} = 30 \times 2^{23} \, \text{Kb/hour} = 251658240 \, \text{Kb/hour}$

Real-World Examples

1. Bandwidth in Data Centers

   • If a data center has a bandwidth of 100 GBps, in base 10, it would be 2.88 $\times 10^{12}$ Kb/hour.

2. High-Speed Internet Connections

   • A high-speed internet connection of 10 GBps can transfer data at the rate of 288 $\times 10^{9}$ Kb/hour in base 10.

3. Server Backup

   • For a server backing up data at 5 GBps, in base 2, it would be able to transfer 1,258,291,200 Kb/hour.

These examples provide a practical sense of how much data can be transferred and illustrate the differences between base 10 and base 2 calculations.