Gigabytes per hour to Tebibits per second conversion

How to convert gigabytes per hour to tebibits per second?

Certainly! Let's break down the conversion process from gigabytes per hour to tebibits per second.

1. Understanding the units:

   • 1 Gigabyte (GB) = 10^9 bytes (base 10)
   • 1 Gibibyte (GiB) = 2^30 bytes (base 2)
   • 1 Tebibit (Tib) = 2^40 bits

2. Base 10 Conversion (using gigabytes with decimal - GB):

   • 1 GB = 10^9 bytes
   • 1 byte = 8 bits
   • 1 hour = 3600 seconds

Step-by-Step Conversion:

1. Convert gigabytes to bits: $1 \text{ GB} \times 10^9 \text{ bytes/GB} \times 8 \text{ bits/byte} = 8 \times 10^9 \text{ bits}$

2. Convert per hour to per second: $8 \times 10^9 \text{ bits/hour} \div 3600 \text{ seconds/hour} = \frac{8 \times 10^9}{3600} \approx 2.222 \times 10^6 \text{ bits/second}$

3. Convert bits to tebibits: $1 \text{ Tib} = 2^{40} \text{ bits}$ $\text{So,} \quad \frac{2.222 \times 10^6 \text{ bits/second}}{2^{40}} \approx 2.222 \times 10^6 \text{ bits/second} \div 1.0995 \times 10^{12}$ $\approx 2.022 \times 10^{-6} \text{ Tib/second}$

4. Base 2 Conversion (using gibibits - GiB):

   • 1 GiB = 2^30 bytes
   • 1 GiB/hour conversion:

Step-by-Step Conversion:

1. Convert gibibytes to bits: $1 \text{ GiB} \times 2^{30} \text{ bytes/GiB} \times 8 \text{ bits/byte} = 8 \times 2^{30} \text{ bits}$
2. Convert per hour to per second: $8 \times 2^{30} \div 3600 \approx 2.222 \times 10^6 \text{ bits/second}$
3. Convert bits to tebibits: $1 \text{ Tib} = 2^{40} \text{ bits}$ $\text{So,} \quad \frac{2.222 \times 10^6 \text{ bits/second}}{2^{40}} = \frac{2.222 \times 10^6}{1.0995 \times 10^{12}} = 2.022 \times 10^{-6} \text{ Tib/second}$

In Summary:

• Base 10 (GB/hour to Tebibits/second): $\approx 2.022 \times 10^{-6} \text{ Tib/second}$

• Base 2 (GiB/hour to Tebibits/second): $\approx 2.222 \times 10^{-6} \text{ Tib/second}$

Real World Examples for Other Quantities of Gigabytes per Hour:

1. Streaming Services:

   • Netflix 4K Streaming: Consumes about 7 GB/hour. $7 \text{ GB/hour} \approx 7 \times 2.022 \times 10^{-6} \text{ Tib/second} = 1.415 \times 10^{-5} \text{ Tib/second}$
   • Amazon Prime (HD): Consumes about 2 GB/hour. $\approx 2 \times 2.022 \times 10^{-6} = 4.044 \times 10^{-6} \text{ Tib/second}$

2. Data Backups:

   • Backup Software: Transfers data at 50 GB/hour. $\approx 50 \times 2.022 \times 10^{-6} = 1.011 \times 10^{-4} \text{ Tib/second}$

3. Internet Speed:

   • Office Network: Transfers files at approximately 10 GB/hour. $\approx 10 \times 2.022 \times 10^{-6} = 2.022 \times 10^{-5} \text{ Tib/second}$

4. Downloading Large Files:

   • Operating System Update: Could be around 4 GB/hour. $\approx 4 \times 2.022 \times 10^{-6} = 8.088 \times 10^{-6} \text{ Tib/second}$

These examples help demonstrate how much data is transferred in various real-world scenarios.