Terabits per day to Gibibits per second conversion

How to convert terabits per day to gibibits per second?

Sure! To convert 1 Terabit per day (Tb/day) to Gibibits per second (Gib/s), you need to understand the relationships between these units of measurement.

Conversion Basics:

1. Time Conversion:

   • There are 24 hours in a day.
   • There are 60 minutes in an hour.
   • There are 60 seconds in a minute.

   So, the total number of seconds in a day $(24 \times 60 \times 60)$ is $86,400$ seconds.

2. Terabit to Gibibit Conversion:

   • Base 10 Conversion:

     • 1 Terabit (Tb) = 1,000,000,000,000 bits (10^12 bits)
     • 1 Gibibit (Gib) = 1,073,741,824 bits (2^30 bits)

   • Base 2 Conversion:

     • 1 Terabit (Tb) = 1,099,511,627,776 bits (2^40 bits, commonly used in computing)

Conversion Step-by-Step:

1. Convert 1 Terabit per day to Terabits per second:

   • $1 \text{ Tb/day} = \frac{1 \text{ Tb}}{86,400 \text{ s}}$

2. Convert Terabits per second to Gibibits per second:

   • Base 10: $1 \text{ Tb/day} = \frac{10^{12} \text{ bits}}{86,400 \text{ s}} \times \frac{1 \text{ Gib}}{1,073,741,824 \text{ bits}}$ $= \frac{10^{12}}{86,400 \times 1,073,741,824} \text{ Gib/s}$ $\approx 0.0107 \text{ Gib/s}$

   • Base 2: $1 \text{ Tb/day} = \frac{2^{40} \text{ bits}}{86,400 \text{ s}} \times \frac{1 \text{ Gib}}{2^{30} \text{ bits}}$ $= \frac{2^{40}}{86,400 \times 2^{30}} \text{ Gib/s}$ $= \frac{2^{10}}{86,400} \text{ Gib/s}$ $\approx 0.0115 \text{ Gib/s}$

Real World Examples for Other Quantities:

1. 5 Terabits per day:

   • Base 10: $5 \times 0.0107 \approx 0.0535 \text{ Gib/s}$
   • Base 2: $5 \times 0.0115 \approx 0.0575 \text{ Gib/s}$

2. 10 Terabits per day:

   • Base 10: $10 \times 0.0107 \approx 0.107 \text{ Gib/s}$
   • Base 2: $10 \times 0.0115 \approx 0.115 \text{ Gib/s}$

3. 100 Terabits per day:

   • Base 10: $100 \times 0.0107 \approx 1.07 \text{ Gib/s}$
   • Base 2: $100 \times 0.0115 \approx 1.15 \text{ Gib/s}$

These examples illustrate how the conversion process allows you to translate a given data transfer rate from Terabits per day to Gibibits per second using either the base 10 or base 2 system.