Gigabits per day to Terabytes per second conversion

How to convert gigabits per day to terabytes per second?

To convert 1 Gigabit per day to Terabytes per second, we'll need to follow a series of steps. Specifically, we'll need to convert time units from days to seconds and data units from Gigabits to Terabytes. Note that the conversion factors differ depending on whether you are using base 10 (decimal) or base 2 (binary) units.

Conversion Framework

1. Convert days to seconds:

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

$1 \text{ day} = 24 \times 60 \times 60 = 86,400 \text{ seconds}$

2. Convert Gigabits to Terabytes (Base 10 and Base 2):

• Base 10:

  • 1 Gigabit (Gb) = $10^9$ bits
  • 1 Terabyte (TB) = $10^{12}$ bytes
  • 1 byte = 8 bits
  • Therefore, 1 TB = $8 \times 10^{12}$ bits

• Base 2:

  • 1 Gigabit (Gb) = $2^{30}$ bits
  • 1 Terabyte (TB) = $2^{40}$ bytes
  • 1 byte = 8 bits
  • Therefore, 1 TB = $8 \times 2^{40}$ bits

Base 10 Conversion

1. Convert 1 Gigabit to bits:

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

2. Convert bits to Terabytes:

$1 \text{ bit} = \frac{1}{8 \times 10^{12}} \text{ TB}$

3. Convert time:

$1 \text{ Gigabit per day} = \frac{10^9}{86,400} \text{ bits per second}$

$1 \text{ Gigabit per day} = \frac{10^9}{86,400 \times 8 \times 10^{12}} \text{ TB per second}$

$= \frac{10^9}{691,200 \times 10^{12}} \text{ TB per second}$

$= \frac{1}{691,200 \times 10^3} \text{ TB per second}$

$\approx 1.446 \times 10^{-9} \text{ TB per second}$

Base 2 Conversion

1. Convert 1 Gigabit to bits:

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

2. Convert bits to Terabytes:

$1 \text{ bit} = \frac{1}{8 \times 2^{40}} \text{ TB}$

3. Convert time:

$1 \text{ Gigabit per day} = \frac{2^{30}}{86,400} \text{ bits per second}$

$1 \text{ Gigabit per day} = \frac{2^{30}}{86,400 \times 8 \times 2^{40}} \text{ TB per second}$

$= \frac{1}{86,400 \times 8 \times 2^{10}} \text{ TB per second}$

$= \frac{1}{86,400 \times 8 \times 1,024} \text{ TB per second}$

$= \frac{1}{707,788,800} \text{ TB per second}$

$\approx 1.412 \times 10^{-9} \text{ TB per second}$

Real-World Examples

Here are some real-world examples with different quantities of Gigabits per day:

1. 10 Gigabits per day:

   • Base 10:
     • Duration conversion: $1 \text{ Gb per day} \approx 1.446 \times 10^{-9} \text{ TB per second}$
     • $10 \text{ Gb per day} \approx 1.446 \times 10^{-8} \text{ TB per second}$
   • Base 2:
     • Duration conversion: $1 \text{ Gb per day} \approx 1.412 \times 10^{-9} \text{ TB per second}$
     • $10 \text{ Gb per day} \approx 1.412 \times 10^{-8} \text{ TB per second}$

2. 100 Gigabits per day:

   • Base 10:
     • $100 \text{ Gb per day} \approx 1.446 \times 10^{-7} \text{ TB per second}$
   • Base 2:
     • $100 \text{ Gb per day} \approx 1.412 \times 10^{-7} \text{ TB per second}$

3. 1 Terabit per day (1,000 Gigabits per day):

   • Base 10:
     • $1,000 \text{ Gb per day} \approx 1.446 \times 10^{-6} \text{ TB per second}$
   • Base 2:
     • $1,000 \text{ Gb per day} \approx 1.412 \times 10^{-6} \text{ TB per second}$

These examples provide a range of data transfer rates that can help in understanding how Gigabits per day convert to Terabytes per second in practical scenarios.