Gigabits per day to Tebibytes per day conversion

How to convert gigabits per day to tebibytes per day?

To convert Gigabits per day (Gb/day) to Tebibytes per day (TiB/day), you first need to understand the differences between the units:

1. Gigabit (Gb):

   • In base 10: 1 Gigabit (Gb) = 10^9 bits
   • In base 2: 1 Gigabit (Gb) = 2^30 bits

2. Tebibyte (TiB):

   • By definition, 1 Tebibyte (TiB) = 2^40 bytes

Base 2 Conversion:

1. Since 1 byte = 8 bits, 1 Tebibyte = 2^40 bytes = 2^40 * 8 bits.
2. Convert Gigabits to Tebibytes: $\text{1 Gigabit in base 2} = 2^{30} \text{bits}$ $\text{1 Tebibyte in bits} = 2^{40} \times 8 = 2^{43} \text{bits}$ $\text{1 Gb/day} = \frac{2^{30} \text{ bits/day}}{2^{43} \text{ bits/TiB}} = 2^{-13} \text{ TiB/day}$ $2^{-13} \approx 0.000122 \text{ TiB/day}$

Base 10 Conversion:

1. Since 1 Gigabit (Gb) = 10^9 bits and 1 Terabyte (TB) = 10^12 bytes, $\text{1 Tebibyte in bits} = 2^{40} \times 8 \approx 8 \times 10^{12} \text{ bits}$ $\text{1 Gb/day} = \frac{10^9 \text{ bits/day}}{8 \times 10^{12} \text{ bits/TiB}} = 1.25 \times 10^{-4} \text{ TiB/day}$ This is approximately the same value derived using base 2 due to the negligible difference for this small scale conversion.

Real-World Examples:

1. 10 Gigabits/day: $10 \text{ Gb/day} \times 0.000122 \approx 0.00122 \text{ TiB/day}$

2. 100 Gigabits/day: $100 \text{ Gb/day} \times 0.000122 \approx 0.0122 \text{ TiB/day}$

3. 1000 Gigabits/day (1 Terabit/day): $1000 \text{ Gb/day} \times 0.000122 \approx 0.122 \text{ TiB/day}$

These quantities give an example of various data transfer rates and how they scale from Gigabits per day to Tebibytes per day.