Gibibytes per day to bits per second conversion

How to convert gibibytes per day to bits per second?

To convert from Gibibytes per day to bits per second, you need to follow several steps aligning the different units involved. Let's break down the conversion process and then compare the results using both base 10 (decimal) and base 2 (binary) systems.

Step-by-Step Conversion

1. Understand the relationship between Gibibytes and bits:

   • 1 Gibibyte (GiB) = 2^30 bytes = 1,073,741,824 bytes.
   • 1 byte = 8 bits.
   • Therefore, 1 GiB = 1,073,741,824 * 8 bits = 8,589,934,592 bits.

2. Convert days to seconds:

   • 1 day = 24 hours.
   • 1 hour = 60 minutes.
   • 1 minute = 60 seconds.
   • Therefore, 1 day = 24 * 60 * 60 = 86,400 seconds.

3. Combine the conversions:

   • To get bits per second, divide the total number of bits by the total number of seconds in a day.

Base 2 Conversion:

• Data in Gibibytes (1 GiB/day)
  • 1 GiB = 8,589,934,592 bits.
• Time (1 day = 86,400 seconds)

So, $\text{Bits per second} = \frac{8,589,934,592 \text{ bits}}{86,400 \text{ seconds}} = 99,581 \text{ bits per second}$

Base 10 Conversion:

• In the base 10 system, 1 Gigabyte (GB) = 10^9 bytes = 1,000,000,000 bytes.
• Therefore, for 1 GB in base 10:
  • 1 GB = 1,000,000,000 bytes * 8 bits/byte = 8,000,000,000 bits.
• Given time (1 day = 86,400 seconds)

So, $\text{Bits per second} = \frac{8,000,000,000 \text{ bits}}{86,400 \text{ seconds}} = 92,592.59 \text{ bits per second}$

Real-World Examples for Other Quantities

1. 10 GiB/day:

   • In base 2: $10 \times 99,581 = 995,810 \text{ bits per second}$
   • In base 10: $10 \times 92,593 = 925,925.9 \text{ bits per second}$

2. 50 GiB/day:

   • In base 2: $50 \times 99,581 = 4,979,050 \text{ bits per second}$
   • In base 10: $50 \times 92,593 = 4,629,629.5 \text{ bits per second}$

3. 100 GiB/day:

   • In base 2: $100 \times 99,581 = 9,958,100 \text{ bits per second}$
   • In base 10: $100 \times 92,593 = 9,259,259 \text{ bits per second}$

These values show the difference in data transfer rates when using base 2 versus base 10. The base 2 values are slightly higher due to the binary system's definition of a gibibyte as opposed to a gigabyte.