Gibibits per day to Terabytes per hour conversion

How to convert gibibits per day to terabytes per hour?

Certainly! Let's break down the process step-by-step.

Step-by-Step Conversion

Definitions:

1 Gibibit (Gib) = 2^30 bits
1 Terabyte (TB) = 10^12 bytes (for base 10) or 2^40 bytes (for base 2)
1 Byte = 8 bits

There are 24 hours in a day.

Conversion to Base 10 (Decimal):

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

2. Convert bits to bytes: $1 \, \text{byte} = 8 \, \text{bits} \quad \Rightarrow \quad 1 \, \text{Gib} = 2^{30} / 8 \, \text{bytes}$

3. Convert bytes to Terabytes (base 10): $1 \, \text{TB (decimal)} = 10^{12} \, \text{bytes}$

4. Combine and simplify: $1 \, \text{Gib} = 2^{30} / 8 \, \text{bytes} \approx 134,217,728 \, \text{bytes}$ $1 \, \text{Gib per day} = \frac{134,217,728 \, \text{bytes}}{10^{12}} \, \text{TB (decimal)} \approx 0.000134 \, \text{TB (decimal)}$

5. Convert to per hour: $1 \, \text{Gib per day} \approx 0.000134 \, \text{TB (decimal)} \div 24 \, \text{hours} \approx 0.000005583 \, \text{TB (decimal)} \, \text{per hour}$

Conversion to Base 2 (Binary):

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

2. Convert bits to bytes: $1 \, \text{byte} = 8 \, \text{bits} \quad \Rightarrow \quad 1 \, \text{Gib} = 2^{30} / 8 \, \text{bytes}$

3. Convert bytes to Terabytes (base 2): $1 \, \text{TB (binary)} = 2^{40} \, \text{bytes}$

4. Combine and simplify: $1 \, \text{Gib} = 2^{30} / 8 \, \text{bytes} = 134,217,728 \, \text{bytes}$ $1 \, \text{Gib per day} = \frac{134,217,728}{2^{40}} \, \text{TB (binary)} \approx 0.000122 \, \text{TB (binary)}$

5. Convert to per hour: $1 \, \text{Gib per day} \approx 0.000122 \, \text{TB (binary)} \div 24 \, \text{hours} \approx 0.000005083 \, \text{TB (binary)} \, \text{per hour}$

Summary:

• Base 10 (Decimal): $1 \, \text{Gib per day} \approx 0.000005583 \, \text{TB (decimal) per hour}$

• Base 2 (Binary): $1 \, \text{Gib per day} \approx 0.000005083 \, \text{TB (binary) per hour}$

Real-World Examples for Other Quantities of Gibibits per day:

1. 10 Gibibits per day:

   • Base 10: $10 \times 0.000005583 \approx 0.00005583$ TB (decimal) per hour.
   • Base 2: $10 \times 0.000005083 \approx 0.00005083$ TB (binary) per hour.

2. 100 Gibibits per day:

   • Base 10: $100 \times 0.000005583 \approx 0.0005583$ TB (decimal) per hour.
   • Base 2: $100 \times 0.000005083 \approx 0.0005083$ TB (binary) per hour.

3. 1,000 Gibibits per day:

   • Base 10: $1,000 \times 0.000005583 \approx 0.005583$ TB (decimal) per hour.
   • Base 2: $1,000 \times 0.000005083 \approx 0.005083$ TB (binary) per hour.

This should give you a comprehensive understanding of how to convert Gibibits per day to Terabytes per hour in both base 10 and base 2.