Gigabits per hour to Tebibits per minute conversion

How to convert gigabits per hour to tebibits per minute?

To convert from Gigabits per hour to Tebibits per minute, we need to understand the definitions and conversion factors between these units.

Base 10 (Decimal) System:

In the base 10 system:

• 1 Gigabit (Gb) = 10^9 bits
• 1 Terabit (Tb) = 10^12 bits

Base 2 (Binary) System:

In the base 2 system:

• 1 Gigabit (Gb) = 2^30 bits
• 1 Tebibit (Tib) = 2^40 bits

Conversion Factors:

• From Gigabits (Gb) to Tebibits (Tib):
  • 1 Gb = 10^9 bits
  • 1 Tib = 2^40 bits
• From hours to minutes:
  • 1 hour = 60 minutes

Conversion Process:

Step-by-Step Conversion for Base 10:

1. Convert Gigabits to bits:

   • $1 \text{ Gb/hour} = 10^9 \text{ bits/hour}$

2. Convert bits to Terabits:

   • $1 \text{ Tb} = 10^{12} \text{ bits}$
   • $1 \text{ hour} = 60 \text{ minutes}$
   • $\text{Terabits per minute} = \frac{10^9 \text{ bits/hour}}{10^{12} \text{ bits/Tb} \times 60 \text{ minutes/hour}}$

3. Simplify:

   • $\frac{10^9}{10^{12} \times 60} = \frac{10^9}{6 \times 10^{13}} = \frac{1}{60,000,000} \text{ Tb/min}$
   • $= 1.6667 \times 10^{-8} \text{ Tb/min}$

Step-by-Step Conversion for Base 2:

1. Convert Gigabits to bits:

   • $1 \text{ Gb/hour} = 2^{30} \text{ bits/hour}$

2. Convert bits to Tebibits:

   • $1 \text{ Tib} = 2^{40} \text{ bits}$
   • $1 \text{ hour} = 60 \text{ minutes}$
   • $\text{Tebibits per minute} = \frac{2^{30} \text{ bits/hour}}{2^{40} \text{ bits/Tib} \times 60 \text{ minutes/hour}}$

3. Simplify:

   • $\frac{2^{30}}{2^{40} \times 60} = \frac{1}{2^{10} \times 60} = \frac{1}{61440} \text{ Tib/min}$
   • $= 1.627604 \times 10^{-5} \text{ Tib/min}$

Real World Examples for Other Quantities of Gigabits per Hour:

1. 10 Gigabits per Hour:

   • Base 10: $10 \times 1.6667 \times 10^{-8} = 1.6667 \times 10^{-7} \text{ Tb/min}$
   • Base 2: $10 \times 1.627604 \times 10^{-5} = 1.627604 \times 10^{-4} \text{ Tib/min}$

2. 50 Gigabits per Hour:

   • Base 10: $50 \times 1.6667 \times 10^{-8} = 8.3335 \times 10^{-7} \text{ Tb/min}$
   • Base 2: $50 \times 1.627604 \times 10^{-5} = 8.13802 \times 10^{-4} \text{ Tib/min}$

3. 100 Gigabits per Hour:

   • Base 10: $100 \times 1.6667 \times 10^{-8} = 1.6667 \times 10^{-6} \text{ Tb/min}$
   • Base 2: $100 \times 1.627604 \times 10^{-5} = 1.627604 \times 10^{-3} \text{ Tib/min}$

This explanation provides a clear understanding of how to convert Gigabits per hour to Tebibits per minute in both base 10 and base 2 systems, along with examples of different quantities.