bits per second to Gigabytes per day conversion

How to convert bits per second to gigabytes per day?

Converting bits per second (bps) to gigabytes per day requires several steps, as you need to account for the different units involved.

1. Convert bits per second to bits per day:

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

   So, the number of seconds in a day is: $60 \times 60 \times 24 = 86,400$

   Therefore, 1 bit per second is equivalent to: $1 \ \text{bps} \times 86,400 \ \text{seconds/day} = 86,400 \ \text{bits/day}$

2. Convert bits to bytes:

   • There are 8 bits in a byte.

   $\frac{86,400 \ \text{bits/day}}{8} = 10,800 \ \text{bytes/day}$

3. Convert bytes to gigabytes:

   This is where it differs between base 10 (decimal) and base 2 (binary):

   Base 10 (Decimal):

   • 1 gigabyte (GB) = 10^9 bytes

   $\frac{10,800 \ \text{bytes/day}}{10^9} = 0.0000108 \ \text{GB/day}$

   Base 2 (Binary):

   • 1 gibibyte (GiB) = 2^30 bytes which equals 1,073,741,824 bytes

   $\frac{10,800 \ \text{bytes/day}}{2^{30}} \approx 0.000010058 \ \text{GiB/day}$

Real-World Examples for Other Data Rates:

1. 100 kilobits per second (kbps):

   • Base 10 (Decimal): $100 \ \text{kbps} \times 86,400 \ \text{seconds/day} = 8,640,000 \ \text{kilobits/day}$ $\frac{8,640,000 \ \text{kilobits/day}}{8,000,000} = 1.08 \ \text{GB/day}$

   • Base 2 (Binary): $1.08 \ \text{GB/day in base 10}$ $\frac{8,640,000 \times 10^3 \ \text{bytes/day}}{2^{30}} \approx 0.00806 \ \text{GiB/day}$

2. 1 Megabit per second (Mbps):

   • Base 10 (Decimal): $1 \ \text{Mbps} \times 86,400 = 86,400,000 \ \text{Megabits/day}$ $\frac{86,400,000 \ \text{megabits/day}}{8,000} = 10.8 \ \text{GB/day}$

   • Base 2 (Binary): $10.8\ \ \text{GB/day in base 10}$ $\frac{86,400,000 \times 10^3 \ \text{bytes/day}}{2^{30}} \approx 8.06 \ \text{GiB/day}$

3. 1 Gigabit per second (Gbps):

   • Base 10 (Decimal): $1 \ \text{Gbps} \times 86,400 = 86,400,000,000 \ \text{Gigabits/day}$ $\frac{86,400,000,000 \ \text{gigabits/day}}{8,000,000,000} = 10.8 \ \text{GB/day}$

   • Base 2 (Binary): $10.8 \ \text{GB/day in base 10}$ $\frac{86,400,000,000 \times 10^3 \ \text{bytes/day}}{2^{30}} \approx 8.06 \ \text{GiB/day}$

This demonstrates how different units and bases affect the conversion outcome, highlighting the importance of specifying which base you're using when dealing with data storage and transfer rates.