Gibibits per day to Tebibits per second conversion

How to convert gibibits per day to tebibits per second?

Certainly! Let's break down the conversion of 1 Gibibit per day to Tebibits per second, and explain both base 10 and base 2 calculations.

Base 2 Conversions

1. Understanding the Units:

   • Gibibit (Gib): 1 Gibibit is $2^{30}$ bits.
   • Tebibit (Tib): 1 Tebibit is $2^{40}$ bits.
   • Day to Second: 1 day = 24 hours = 24 * 60 minutes = 1440 minutes = 1440 * 60 seconds = 86400 seconds.

2. Convert Gibibits per Day to Bits per Second:

   • Start with 1 Gibibit/day.
   • Convert Gibibits to bits: $1 \text{ Gib} = 2^{30} \text{ bits}$.
   • Convert days to seconds: 1 day = 86400 seconds.

   $\frac{1 \text{ Gib}}{1 \text{ day}} = \frac{2^{30} \text{ bits}}{86400 \text{ seconds}}$

3. Calculate the Bits per Second:

   $\frac{2^{30} \text{ bits}}{86400 \text{ seconds}} = \frac{1073741824 \text{ bits}}{86400 \text{ seconds}} \approx 12419.4775 \text{ bits/second}$

4. Convert Bits per Second to Tebibits per Second:

   • Convert bits to Tebibits: $1 \text{ Tib} = 2^{40} \text{ bits}$.

   $\frac{12419.4775 \text{ bits/second}}{2^{40}} = \frac{12419.4775 \text{ bits/second}}{1099511627776} \approx 1.129 \times 10^{-8} \text{ Tib/second}$

Base 10 Conversions

In the base 10 (decimal) system, the conversion would use the decimal definitions of the units:

1. Understanding the Units:

   • Gigabit (Gb in base 10): 1 Gigabit is $10^9$ bits.
   • Terabit (Tb in base 10): 1 Terabit is $10^{12}$ bits.
   • Day to Second: 1 day = 86400 seconds.

2. Convert Gigabits per Day to Bits per Second:

   • Start with 1 Gigabit/day.
   • Convert Gigabits to bits: $1 \text{ Gb} = 10^9 \text{ bits}$.
   • Convert days to seconds: 1 day = 86400 seconds.

   $\frac{1 \text{ Gb}}{1 \text{ day}} = \frac{10^9 \text{ bits}}{86400 \text{ seconds}}$

3. Calculate the Bits per Second:

   $\frac{10^9 \text{ bits}}{86400 \text{ seconds}} \approx 11574.0741 \text{ bits/second}$

4. Convert Bits per Second to Terabits per Second:

   • Convert bits to Terabits: $1 \text{ Tb} = 10^{12} \text{ bits}$.

   $\frac{11574.0741 \text{ bits/second}}{10^{12}} \approx 1.157 \times 10^{-8} \text{ Tb/second}$

Real World Examples

To put things in perspective, here are some real-world examples for other quantities of Gibibits per day:

1. 10 Gibibits per Day:

   • Base 2: $\approx 1.24195 \times 10^{-7} \text{ Tib/second}$
   • Base 10: $\approx 1.157 \times 10^{-7} \text{ Tb/second}$

2. 100 Gibibits per Day (equivalent to 12.4195 Kibibits per second in base 2):

   • Base 2: $\approx 1.24195 \times 10^{-6} \text{ Tib/second}$
   • Base 10: $\approx 1.157 \times 10^{-6} \text{ Tb/second}$

3. 1000 Gibibits per Day:

   • Base 2: $\approx 1.24195 \times 10^{-5} \text{ Tib/second}$
   • Base 10: $\approx 1.157 \times 10^{-5} \text{ Tb/second}$

Summary

• Base 2 (Binary) Conversion:

  • 1 Gibibit/day ≈ $1.129 \times 10^{-8} \text{ Tib/second}$

• Base 10 (Decimal) Conversion:

  • 1 Gigabit/day ≈ $1.157 \times 10^{-8} \text{ Tb/second}$

I hope this explanation helps! If you need any further details, feel free to ask!