Gigabits per day to Terabits per hour conversion

How to convert gigabits per day to terabits per hour?

Converting gigabits per day to terabits per hour involves several steps. Let's go through each of them, considering both base 10 and base 2.

1. Base 10 (Decimal System)

Step 1: Understand the units

• 1 day = 24 hours
• 1 terabit (Tb) = 1,000 gigabits (Gb)

Step 2: Convert gigabits per day to gigabits per hour

$\text{Gigabits per hour} = \frac{\text{Gigabits per day}}{\text{Hours per day}} = \frac{1 \text{ Gb/day}}{24 \text{ hr/day}} = \frac{1}{24} \text{ Gb/hr}$

Step 3: Convert gigabits per hour to terabits per hour

$\text{Terabits per hour} = \frac{\text{Gigabits per hour}}{1,000 \text{ Gb/Tb}} = \frac{\frac{1}{24} \text{ Gb/hr}}{1,000 \text{ Gb/Tb}} = \frac{1}{24,000} \text{ Tb/hr}$

So, 1 Gigabit per day is approximately $4.167 \times 10^{-5}$ Terabits per hour in base 10.

2. Base 2 (Binary System)

Step 1: Understand the units

• Still, 1 day = 24 hours
• 1 terabit (TiB) = 1,024 gigabits (GiB)

Step 2: Convert gigabits per day to gigabits per hour

$\text{Gigabits per hour} = \frac{1 \text{ GiB/day}}{24 \text{ hr/day}} = \frac{1}{24} \text{ GiB/hr}$

Step 3: Convert gigabits per hour to terabits per hour

$\text{Terabits per hour} = \frac{\frac{1}{24} \text{ GiB/hr}}{1,024 \text{ GiB/TiB}} = \frac{1}{24 \times 1,024} \text{ TiB/hr} = \frac{1}{24,576} \text{ TiB/hr}$

So, 1 Gigabit per day is approximately $4.069 \times 10^{-5}$ Terabits per hour in base 2.

Real-World Examples

1. 10 Gigabits per Day

• Base 10: $10 \times 4.167 \times 10^{-5} = 4.167 \times 10^{-4} \text{ Tb/hr}$
• Base 2: $10 \times 4.069 \times 10^{-5} = 4.069 \times 10^{-4} \text{ TiB/hr}$

2. 100 Gigabits per Day

• Base 10: $100 \times 4.167 \times 10^{-5} = 4.167 \times 10^{-3} \text{ Tb/hr}$
• Base 2: $100 \times 4.069 \times 10^{-5} = 4.069 \times 10^{-3} \text{ TiB/hr}$

3. 1,000 Gigabits per Day (1 Terabit per Day)

• Base 10: $1,000 \times 4.167 \times 10^{-5} = 0.04167 \text{ Tb/hr}$
• Base 2: $1,000 \times 4.069 \times 10^{-5} = 0.04069 \text{ TiB/hr}$

Summary

• Base 10: 1 Gb/day ≈ 4.167 × 10⁻⁵ Tb/hr
• Base 2: 1 GiB/day ≈ 4.069 × 10⁻⁵ TiB/hr

These conversions help you understand how to scale data rates across different time units and magnitudes in both base 10 and base 2 systems.