Gibibytes per second to Kilobits per day conversion

How to convert gibibytes per second to kilobits per day?

Converting 1 Gibibyte per second (GiB/s) to Kilobits per day involves several steps and requires an understanding of both base-2 and base-10 systems. Let's work this out step by step for each system.

Base-2 System (Binary System)

1 Gibibyte (GiB) = 2^30 bytes 1 byte = 8 bits 1 second = 86400 seconds (since there are 24 hours in a day, 60 minutes in an hour, and 60 seconds in a minute).

Steps:

1. Convert GiB to bytes: $1 \text{ GiB} = 2^{30} \text{ bytes} = 1,073,741,824 \text{ bytes}$

2. Convert bytes to bits: $1,073,741,824 \text{ bytes} \times 8 \text{ bits/byte} = 8,589,934,592 \text{ bits}$

3. Convert bits per second to bits per day: $8,589,934,592 \text{ bits/second} \times 86,400 \text{ seconds/day} = 742,325,409,792,000 \text{ bits/day}$

4. Convert bits to Kilobits (Kb): $742,325,409,792,000 \text{ bits} \div 1,024 \text{ bits/Kilobit} = 724,775,731,200 \text{ Kilobits/day}$

Therefore, in the base-2 system, $1 \text{ GiB/s} = 724,775,731,200 \text{ Kb/day}$

Base-10 System (Decimal System)

1 Gigabyte (GB) = 10^9 bytes 1 byte = 8 bits 1 second = 86400 seconds.

Steps:

1. Convert GB to bytes: $1 \text{ GB} = 10^9 \text{ bytes} = 1,000,000,000 \text{ bytes}$

2. Convert bytes to bits: $1,000,000,000 \text{ bytes} \times 8 \text{ bits/byte} = 8,000,000,000 \text{ bits}$

3. Convert bits per second to bits per day: $8,000,000,000 \text{ bits/second} \times 86,400 \text{ seconds/day} = 691,200,000,000,000 \text{ bits/day}$

4. Convert bits to Kilobits (Kb): $691,200,000,000,000 \text{ bits} \div 1,000 \text{ bits/Kilobit} = 691,200,000,000 \text{ Kilobits/day}$

Therefore, in the base-10 system, $1 \text{ GB/s} = 691,200,000,000 \text{ Kb/day}$

Real-World Examples

1. 5 GiB/s:

   • Base-2: $5 \times 724,775,731,200 \text{ Kb/day} = 3,623,878,656,000 \text{ Kb/day}$
   • Base-10: $5 \times 691,200,000,000 \text{ Kb/day} = 3,456,000,000,000 \text{ Kb/day}$

2. 0.5 GiB/s:

   • Base-2: $0.5 \times 724,775,731,200 \text{ Kb/day} = 362,387,865,600 \text{ Kb/day}$
   • Base-10: $0.5 \times 691,200,000,000 \text{ Kb/day} = 345,600,000,000 \text{ Kb/day}$

3. 10 GiB/s:

   • Base-2: $10 \times 724,775,731,200 \text{ Kb/day} = 7,247,757,312,000 \text{ Kb/day}$
   • Base-10: $10 \times 691,200,000,000 \text{ Kb/day} = 6,912,000,000,000 \text{ Kb/day}$

These conversions illustrate the differences between the binary and decimal systems, as well as the immense data transfer rates that modern networks are capable of handling.