Gigabits per day to Tebibytes per hour conversion

How to convert gigabits per day to tebibytes per hour?

Sure, I'll walk you through the process of converting 1 Gigabit per day to Tebibytes per hour, and provide explanations for both base 10 (decimal) and base 2 (binary) systems.

Conversion Steps

Understanding Units

1. Gigabit (Gb): 1 Gigabit = 1,000,000,000 bits (base 10) or 2^30 bits (1,073,741,824 bits in base 2).
2. Tebibyte (TiB): 1 Tebibyte = 2^40 bytes = 1,099,511,627,776 bytes = 8,796,093,022,208 bits.

Conversion for Base 10

1. Gigabits per Day to Gigabits per Hour: $\text{1 Gigabit/day} \times \frac{1 \text{ day}}{24 \text{ hours}} = \frac{1}{24} \text{ Gigabits per hour}$

2. Gigabits per Hour to Tebibytes per Hour: $\frac{1 \text{ Gigabit}}{24 \text{ hours}} \times \frac{1,000,000,000 \text{ bits}}{1 \text{ Gigabit}} \times \frac{1 \text{ Tebibyte}}{8,796,093,022,208 \text{ bits}} = \frac{1,000,000,000}{24 \times 8,796,093,022,208} \text{ Tebibytes per hour}$ Simplify the calculation: $\frac{1,000,000,000}{211,146,232,531.2} \approx 4.735 \times 10^{-6} \ \text{ Tebibytes per hour}$

Conversion for Base 2

1. Gigabits per Day to Gigabits per Hour: $\text{1 Gibibit/day} \times \frac{1 \text{ day}}{24 \text{ hours}} = \frac{1}{24} \text{ Gibibits per hour}$

2. Gigabits per Hour to Tebibytes per Hour: $\frac{1 \text{ Gibibit}}{24 \text{ hours}} \times \frac{1,073,741,824 \text{ bits}}{1 \text{ Gibibit}} \times \frac{1 \text{ Tebibyte}}{8,796,093,022,208 \text{ bits}} = \frac{1,073,741,824}{24 \times 8,796,093,022,208} \text{ Tebibytes per hour}$ Simplify the calculation: $\frac{1,073,741,824}{211,146,232,531.2} \approx 5.087 \times 10^{-6} \ \text{ Tebibytes per hour}$

Summary Answer

• Base 10 System: $\approx 4.735 \times 10^{-6}$ Tebibytes per hour.
• Base 2 System: $\approx 5.087 \times 10^{-6}$ Tebibytes per hour.

Real World Examples

1. 50 Gigabits per day:

   • Base 10: $50 \times 4.735 \times 10^{-6} \approx 2.368 \times 10^{-4}$ Tebibytes per hour.
   • Base 2: $50 \times 5.087 \times 10^{-6} \approx 2.544 \times 10^{-4}$ Tebibytes per hour.

2. 200 Gigabits per day:

   • Base 10: $200 \times 4.735 \times 10^{-6} \approx 9.470 \times 10^{-4}$ Tebibytes per hour.
   • Base 2: $200 \times 5.087 \times 10^{-6} \approx 10.174 \times 10^{-4}$ Tebibytes per hour.

3. 1 Terabit (1000 Gigabits) per day:

   • Base 10: $1000 \times 4.735 \times 10^{-6} \approx 4.735 \times 10^{-3}$ Tebibytes per hour.
   • Base 2: $1000 \times 5.087 \times 10^{-6} \approx 5.087 \times 10^{-3}$ Tebibytes per hour.

These examples illustrate how much data can be transferred over different periods and scales, making it easier to understand network capabilities and requirements for various applications.