Gibibits per hour to Terabytes per second conversion

How to convert gibibits per hour to terabytes per second?

To convert Gibibits per hour (Gibibit/h) to Terabytes per second (TB/s), you need to understand the difference between bits and bytes, as well as the difference between the base-10 (decimal) and base-2 (binary) systems.

1 Gibibit (Gib) = 2^30 bits (binary prefix) 1 Terabyte (TB) = 10^12 bytes (decimal prefix) or 2^40 bytes (binary prefix) 1 Byte = 8 bits

Base 2 (Binary) System

1 Gibit (Gib) = 2^30 bits 1 TiB (Tebibyte) = 2^40 bytes 1 Byte = 8 bits 1 TiB (Tebibyte) = 2^40 * 8 bits = 2^43 bits

Step-by-Step Calculation:

1. Convert Gibibits to bits: $1 \text{ Gibibit} = 2^{30} \text{ bits}$

2. Convert bits to Tebibytes: $2^{30} \text{ bits} = \left( 2^{30} / 2^{43} \right) \text{ TiB} = 2^{-13} \text{ TiB}$

3. Convert hours to seconds: $1 \text{ hour} = 3600 \text{ seconds}$

4. Finally, combine everything: $\left( 2^{-13} \text{ TiB} \right) / 3600 \text{ seconds} = 2^{-13} / 3600 \text{ TiB/s} = 3.005 \times 10^{-17} \text{ TiB/s}$

Base 10 (Decimal) System

1 Gibit (Gib) = 2^30 bits 1 TB (Terabyte) = 10^12 bytes 1 Byte = 8 bits 1 TB (Terabyte) = 10^12 * 8 bits = 8 * 10^12 bits

Step-by-Step Calculation:

1. Convert Gibibits to bits: $1 \text{ Gibibit} = 2^{30} \text{ bits}$

2. Convert bits to Terabytes: $2^{30} \text{ bits} = \left( 2^{30} / 8 \times 10^{12} \right) \text{ TB} = \left( 2^{30} / 8 \times 10^{12} \right) \text{ TB}$ $2^{30} = 1073741824 \approx 1.074 \times 10^9$ $\approx (1.074 \times 10^9 ) / (8 \times 10^{12})$ $\approx 1.34 \times 10^{-4} \text{ TB}$

3. Convert hours to seconds: $1 \text{ hour} = 3600 \text{ seconds}$

4. Finally, combine everything: $\left( 1.34 \times 10^{-4} \text{ TB} \right) / 3600 \text{ seconds}$ $\approx 3.72 \times 10^{-8} \text{ TB/s}$

Real-World Examples

1. Home Internet Usage: Let's say an average home internet plan offers 100 Gibibit per hour download speed.

   $100 \text{ Gibibits/hour} \implies 100 \times (2^{-13} / 3600) \text{ TiB/s} \approx 3.005 \times 10^{-15} \text{ TiB/s}$ $\approx 3.72 \times 10^{-6} \text{ TB/s}$

2. Corporate Network: A corporate network might have an internal data transfer rate of 20,000 Gibibits per hour. $20,000 \text{ Gibibits/hour} \approx 7.305 \times 10^{-12} \text{ TiB/s}$ $\approx 7.44 \times 10^{-4} \text{ TB/s}$

3. Data Centers: Data centers might transfer data at rates up to 10,000,000 Gibibits per hour. $10,000,000 \text{ Gibibits/hour} \approx 3.005 \times 10^{-8} \text{ TiB/s}$ $\approx 3.72 \text{ TB/s}$

Always make sure to specify which base you are using because it affects the conversion factor. In the tech industry, the binary (base 2) system is often used for memory and storage, while networking equipment might use decimal (base 10) measurements.