bits per second to Kibibits per day conversion

How to convert bits per second to kibibits per day?

To convert from bits per second (bps) to Kibibits per day, we'll go through a series of conversion steps. First, let's understand the base 10 and base 2 conversions:

Base 10 (Decimal) Conversion

1. Bits to Kilobits:

   • 1 Kilobit (Kb) = 10^3 bits = 1000 bits
   • Therefore, 1 bps = $\frac{1}{1000}$ Kilobits per second (Kb/s).

2. Seconds to Days:

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

3. Calculate Kilobits per Day:

   • Since 1 bps = 1/1000 Kb/s, in one day:
   • $\frac{1}{1000}$ Kb/s * 86,400 seconds = 86.4 Kilobits per day.

4. Kilobits to Kibibits:

   • Note: In base 10, we typically stay in Kilobits. However, for the sake of consistency:
   • 1 Kilobit = 10^3 bits.
   • 1 Kibibit = 2^10 bits = 1024 bits.
   • So, 1 Kilobit = $\frac{1000}{1024}$ Kibibits ≈ 0.9765625 Kibibits.

   Convert Kilobits to Kibibits:

   • 86.4 Kilobits/day * 0.9765625 Kibibits/Kilobit = 84.375 Kibibits per day.

Base 2 (Binary) Conversion

1. Bits to Kibibits:

   • 1 Kibibit (Kibit) = 2^10 bits = 1024 bits.
   • Therefore, 1 bps = $\frac{1}{1024}$ Kibibits per second (Kibit/s).

2. Seconds to Days:

   • Same calculation as above: 1 day = 86,400 seconds.

3. Calculate Kibibits per Day:

   • Since 1 bps = 1/1024 Kibit/s, in one day:
   • $\frac{1}{1024}$ Kibit/s * 86,400 seconds = approximately 84.375 Kibibits per day.

Summary

• Base 10 Conversion: 1 bps ≈ 84.375 Kibibits/day.
• Base 2 Conversion: 1 bps ≈ 84.375 Kibibits/day.

Real World Examples

• 10 Mbps (10 Megabits per second):
  • Base 10: $10 \times 10^6$ bps.
  • Base 2: $10 \times 2^{20}$ bps.
  • Converting to Kibibits per day (in base 10):
    • 10,000,000 bps * $\frac{1}{1000}$ Kb/bps * 0.9765625 Kibibytes/Kb * 86,400 s/day ≈ 864,375,000 Kibibits/day.
• 1 Gbps (1 Gigabit per second):
  • Base 10: $1 \times 10^9$ bps.
  • Base 2: $1 \times 2^{30}$ bps.
  • Converting to Kibibits per day (in base 10):
    • 1,000,000,000 bps * $\frac{1}{1000}$ Kb/bps * 0.9765625 Kibibytes/Kb * 86,400 s/day ≈ 86,437,500,000 Kibibits/day.

These conversions give you an idea of the data transfer capabilities over various time periods and using different bases of calculation.