Gibibits per minute to Tebibytes per day conversion

How to convert gibibits per minute to tebibytes per day?

Sure, I'd be happy to help you with the conversion and provide some examples!

Understanding the Units

• Gibibit (Gib): A binary unit of data equal to $2^{30}$ bits.
• Tebibyte (TiB): A binary unit of data equal to $2^{40}$ bytes.
• Minute to Day: 1 day = 1440 minutes.

Conversion Steps

Base 2 (Binary)

1. Convert Gibibits to Gibibytes:

   • $1 \text{ Gibibit} = 1 / 8 \text{ Gibibytes}$ (because there are 8 bits in a byte).
   • Therefore, $1 \text{ Gibibit per minute} = 1/8 \text{ Gibibytes per minute}$.

2. Convert Gibibytes to Tebibytes:

   • $1 \text{ Gibibyte} = 2^{-10} \text{ Tebibytes}$.
   • Hence, $(1/8) \text{ GiB} = (1/8) \times (2^{-10}) \text{ TiB} = \frac{1}{8192} \text{ TiB per minute}$.

3. Convert per minute rate to per day rate:

   • There are 1440 minutes in a day.
   • So, $\frac{1}{8192} \text{ TiB per minute} \times 1440 \text{ minutes per day} = \frac{1440}{8192} \text{ TiB per day}$.
   • Simplify: $\frac{1440}{8192} = 0.17578125 \text{ TiB per day}$.

Real-World Examples of Other Quantities in Base 2

• 5 Gibibits per minute:

  • $5 \times 0.17578125 = 0.87890625 \text{ TiB per day}$.

• 10 Gibibits per minute:

  • $10 \times 0.17578125 = 1.7578125 \text{ TiB per day}$.

• 100 Gibibits per minute:

  • $100 \times 0.17578125 = 17.578125 \text{ TiB per day}$.

Conversion in Base 10 (Decimal)

If we consider the base 10 definitions where:

• 1 Gigabit (Gb) = $10^9$ bits,
• 1 Terabyte (TB) = $10^{12}$ bytes.

Steps

1. Convert Gigabits to Gigabytes:

   • $1 \text{ Gigabit} = 1 / 8 \text{ Gigabytes}$, because there are 8 bits in a byte.

2. Convert Gigabytes to Terabytes:

   • $1 \text{ Gigabyte} = 10^{-3} \text{ Terabytes}$.

3. Convert per minute rate to per day rate:

   • $1 \text{ Gigabit per minute} \rightarrow (1/8) \text{ Gigabytes per minute} \rightarrow (1/8) \times 10^{-3} \text{ Terabytes per day}$.
   • $\frac{1}{8} \times 10^{-3} \text{ Terabytes per minute} = \frac{1}{8000} \text{ Terabytes per minute}$.
   • Multiply by the number of minutes in a day (1440): $\frac{1440}{8000} = 0.18 \text{ Terabytes per day}$.

Real-World Examples in Base 10

• 5 Gigabits per minute:

  • $5 \times 0.18 = 0.90 \text{ TB per day}$.

• 10 Gigabits per minute:

  • $10 \times 0.18 = 1.80 \text{ TB per day}$.

• 100 Gigabits per minute:

  • $100 \times 0.18 = 18 \text{ TB per day}$.

Conclusion

In summary:

• 1 Gibibit per minute equals approximately 0.17578125 Tebibytes per day (binary).
• 1 Gigabit per minute equals 0.18 Terabytes per day (decimal).

The real-world examples scale linearly as shown.