Gibibytes per day to Tebibits per day conversion

How to convert gibibytes per day to tebibits per day?

To convert Gibibytes per day (GiB/day) to Tebibits per day (Tibit/day), you'll need to understand the relationships between the units, specifically the difference between base 2 and base 10.

Base 2 (Binary System)

1 Gibibyte (GiB) is $2^{30}$ bytes. 1 Tebibit (Tibit) is $2^{40}$ bits.

Step-by-Step Conversion:

1. Convert Gibibytes to bits:

   • 1 GiB = $2^{30}$ bytes
   • 1 byte = 8 bits
   • Therefore, 1 GiB = $2^{30} \times 8$ bits

   $1 \text{ GiB} = 2^{30} \times 8 = 2^{33} \text{ bits}$

2. Convert bits to Tebibits:

   • 1 Tibit = $2^{40}$ bits
   • Therefore:

   $1 \text{ GiB} = \frac{2^{33} \text{ bits}}{2^{40} \text{ bits/Tibit}}$

   Simplifying:

   $1 \text{ GiB} = 2^{33 - 40} \text{ Tibit} = 2^{-7} \text{ Tibit} = \frac{1}{128} \text{ Tibit}$

So, 1 GiB/day = $\frac{1}{128}$ Tibit/day.

Base 10 (Decimal System)

Note that in standard metric (SI) units, Terabit (Tbit) and gigabyte (GB) are used instead of Tebibit and Gibibyte:

• 1 Gigabyte (GB) = $10^9$ bytes
• 1 Terabit (Tbit) = $10^{12}$ bits

However, conversion in base 10 is not typically standard for Tebibits and Gibibytes but let's complete the conversion for educational purposes.

Step-by-Step Conversion (decimal-based):

1. Convert Gibibytes to bits:

   • 1 GiB = $1.073741824 \times 10^9$ bytes (approx)
   • 1 byte = 8 bits
   • Therefore, 1 GiB = $1.073741824 \times 10^9 \times 8$ bits

   $1 \text{ GiB} = 8.589934592 \times 10^9 \text{ bits}$

2. Convert bits to Terabits:

   • 1 Tbit = $10^{12}$ bits
   • Therefore:

   $1 \text{ GiB} = \frac{8.589934592 \times 10^9 \text{ bits}}{10^{12} \text{ bits/Tbit}}$

   Simplifying:

   $1 \text{ GiB} = 0.008589934592 \text{ Tbit}$

So, 1 GiB/day in decimal terms converts to approximately $0.00859$ Tbit/day.

Real World Examples for Different Quantities of Gibibytes per Day

1. 10 GiB/day:

   • Base 2: $10 \text{ GiB/day} = 10 \times \frac{1}{128} \text{ Tibit/day} = \frac{10}{128} \text{ Tibit/day} \approx 0.078125 \text{ Tibit/day}$
   • Base 10: $10 \text{ GiB/day} = 10 \times 0.008589 \text{ Tbit/day} = 0.08589 \text{ Tbit/day}$

2. 100 GiB/day:

   • Base 2: $100 \text{ GiB/day} = 100 \times \frac{1}{128} \text{ Tibit/day} = \frac{100}{128} \text{ Tibit/day} \approx 0.78125 \text{ Tibit/day}$
   • Base 10: $100 \text{ GiB/day} = 100 \times 0.008589 \text{ Tbit/day} = 0.8589 \text{ Tbit/day}$

3. 1,000 GiB/day:

   • Base 2: $1{000} \text{ GiB/day} = 1{000} \times \frac{1}{128} \text{ Tibit/day} = \frac{1{000}}{128} \text{ Tibit/day} \approx 7.8125 \text{ Tibit/day}$
   • Base 10: $1{000} \text{ GiB/day} = 1{000} \times 0.008589 \text{ Tbit/day} = 8.589 \text{ Tbit/day}$

These conversions help you understand how to translate data transfer rates in different units of measure, whether you are using base 2 for computer storage or base 10 for telecommunications.