Gibibits per hour to Terabytes per day conversion

How to convert gibibits per hour to terabytes per day?

Sure! Let's begin by breaking down the conversions step by step. First, we need to understand the relationships between the units involved.

Definitions and Relationships

1 Gibibit (Gib) is equivalent to 2^30 bits. 1 Terabyte (TB) is 10^12 bytes (base 10) or 2^40 bytes (base 2).

There are:

• 1 byte = 8 bits
• 1 hour = 3600 seconds
• 1 day = 24 hours

Step-by-Step Conversion

Step 1: Convert Gibibits per hour to bits per hour

1 Gibibit/hour = 2^30 bits/hour

Step 2: Convert bits per hour to bits per day

Since there are 24 hours in a day: $2^{30} \text{ bits/hour} \times 24 \text{ hours/day} = 2^{30} \times 24 \text{ bits/day}$

Step 3: Convert bits per day to bytes per day

1 byte = 8 bits, so: $\frac{2^{30} \times 24}{8} \text{ bytes/day} = 2^{30} \times 3 \text{ bytes/day}$

Step 4: Convert bytes per day to Terabytes per day

Base 10 (Decimal)

1 Terabyte (TB) = 10^12 bytes: $\frac{2^{30} \times 3}{10^{12}} \text{ TB/day} = \frac{3 \times 2^{30}}{10^{12}} \text{ TB/day} \approx \frac{3 \times 10^{9}}{10^{12}} \text{ TB/day} \approx 0.003 \text{ TB/day}$

Base 2 (Binary)

1 Terabyte (TB) = 2^40 bytes: $\frac{2^{30} \times 3}{2^{40}} \text{ TB/day} = \frac{3 \times 2^{30}}{2^{40}} \text{ TB/day} = 3 \times 2^{-10} \text{ TB/day} = 3 \times \frac{1}{1024} \text{ TB/day} \approx 0.00293 \text{ TB/day}$

Summary

• In base 10 (Decimal): 1 Gibibit per hour equals approximately 0.003 Terabytes per day.
• In base 2 (Binary): 1 Gibibit per hour equals approximately 0.00293 Terabytes per day.

Real-world Examples of Gibibits per Hour

10 Gibibits per hour

• Base 10: $10 \times 0.003 \text{ TB/day} = 0.03 \text{ TB/day}$
• Base 2: $10 \times 0.00293 \text{ TB/day} \approx 0.0293 \text{ TB/day}$

50 Gibibits per hour

• Base 10: $50 \times 0.003 \text{ TB/day} = 0.15 \text{ TB/day}$
• Base 2: $50 \times 0.00293 \text{ TB/day} \approx 0.1465 \text{ TB/day}$

100 Gibibits per hour

• Base 10: $100 \times 0.003 \text{ TB/day} = 0.3 \text{ TB/day}$
• Base 2: $100 \times 0.00293 \text{ TB/day} \approx 0.293 \text{ TB/day}$

These examples illustrate how varying amounts of Gibibits per hour translate into Terabytes per day, using both base 10 and base 2 calculations.