bits per day to Gigabits per second conversion

How to convert bits per day to gigabits per second?

Sure! Converting bits per day (b/d) to Gigabits per second (Gbps) involves several steps. Let's break it down:

Step-by-Step Conversion

1. Convert days to seconds: Since there are 24 hours in a day, 60 minutes in an hour, and 60 seconds in a minute: $1 \text{ day} = 24 \times 60 \times 60 \text{ seconds} = 86400 \text{ seconds}$

2. Convert bits to Gigabits:

   • In base 10 (decimal), 1 Gigabit (Gb) = $10^9$ bits.
   • In base 2 (binary), 1 Gibibit (Gib) = $2^{30}$ bits = 1,073,741,824 bits.

Convert 1 bit per day to Gbps:

Using base 10:

$\frac{1 \text{ bit/day}}{86400 \text{ seconds/day}} = 1.15740741 \times 10^{-5} \text{ bits/second}$

Next, convert bits per second to Gigabits per second: $1.15740741 \times 10^{-5} \text{ bits/second} \times \frac{1 \text{ Gigabit}}{10^9 \text{ bits}} = 1.15740741 \times 10^{-14} \text{ Gbps}$

Using base 2:

$\frac{1 \text{ bit/day}}{86400 \text{ seconds/day}} = 1.15740741 \times 10^{-5} \text{ bits/second}$

Next, convert bits per second to Gibibits per second: $1.15740741 \times 10^{-5} \text{ bits/second} \times \frac{1 \text{ Gibibit}}{2^{30} \text{ bits}} = 1.0782 \times 10^{-15} \text{ Gibibits/second}$

Real World Examples

1. Internet Bandwidth:

• 100 Megabits per day:
  • Base 10: $\frac{100 \times 10^6 \text{ bits/day}}{86400 \text{ seconds/day}} \times \frac{1 \text{ Gigabit}}{10^9 \text{ bits}} = \frac{10^5}{86400} \approx 1.1574 \times 10^{-3} \text{ Gbps}$
  • Base 2: $\frac{100 \times 2^{20} \text{ bits/day}}{86400 \text{ seconds/day}} \times \frac{1 \text{ Gibibit}}{2^{30} \text{ bits}} = \frac{100 \times 2^{20}}{86400 \times 2^{30}} \approx 1.0782 \times 10^{-6} \text{ Gibibits/second}$

2. Data Transfer for Large Files:

• 1 Terabit per day:
  • Base 10: $\frac{1 \times 10^{12} \text{ bits/day}}{86400 \text{ seconds/day}} \times \frac{1 \text{ Gigabit}}{10^9 \text{ bits}} \approx 11.574 \text{ Gbps}$
  • Base 2: $\frac{1 \times 2^{40} \text{ bits/day}}{86400 \text{ seconds/day}} \times \frac{1 \text{ Gibibit}}{2^{30} \text{ bits}} \approx 1.078 \text{ Gibibits/second}$

These examples give you an idea of how different quantities of bits per day can translate into data transfer rates in terms of Gigabits per second, using both base 10 and base 2 conventions.