Kilobits per day to Gibibytes per second conversion

How to convert kilobits per day to gibibytes per second?

Sure! Let's go through the steps to convert 1 Kilobit per day to Gibibytes per second.

Step-by-Step Conversion

Base 10 (Decimal)

1. Convert Kilobits to Bits:

   • 1 Kilobit (Kb) = 1 * 10^3 bits (Decimal system) = 1,000 bits.

2. Convert Days to Seconds:

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

3. Convert Bits per Day to Bits per Second:

   • 1,000 bits/day divided by 86,400 seconds/day
   • $\frac{1,000 \text{ bits}}{86,400 \text{ seconds}} \approx 0.0115741 \text{ bits/second}$

4. Convert Bits per Second to Bytes per Second:

   • 1 byte = 8 bits
   • $\frac{0.0115741 \text{ bits/second}}{8} \approx 0.00144676 \text{ bytes/second}$

5. Convert Bytes per Second to Gigabytes per Second:

   • 1 Gigabyte (GB) = 10^9 bytes
   • $\frac{0.00144676 \text{ bytes/second}}{10^9} \approx 1.44676 \times 10^{-12} \text{ GB/second}$

6. Convert Gigabytes to Gibibytes:

   • 1 Gibibyte (GiB) = $2^{30}$ bytes = 1,073,741,824 bytes
   • $\frac{0.00144676\ \text{ bytes/second}}{1,073,741,824} \approx 1.3477 \times 10^{-12}\ \text{ GiB/second}$

Therefore, for the Decimal system: 1 Kilobit per day ≈ 1.3477 x $10^{-12}$ Gibibytes per second.

Base 2 (Binary)

1. Convert Kilobits to Bits:

   • 1 Kibibit (Kibit) = 1 * 2^10 bits = 1,024 bits.

2. Convert Days to Seconds:

   • (This step is the same in both systems)
   • Total seconds in a day = 86,400 seconds.

3. Convert Bits per Day to Bits per Second:

   • 1,024 bits/day divided by 86,400 seconds/day
   • $\frac{1,024 \text{ bits}}{86,400 \text{ seconds}} \approx 0.0118519\ \text{ bits/second}$

4. Convert Bits per Second to Bytes per Second:

   • 1 byte = 8 bits
   • $\frac{0.0118519 \text{ bits/second}}{8} \approx 0.00148149\ \text{ bytes/second}$

5. Convert Bytes per Second to Gibibytes per Second:

   • 1 Gibibyte (GiB) = $2^{30}$ bytes = 1,073,741,824 bytes
   • $\frac{0.00148149\ \text{ bytes/second}}{1,073,741,824} \approx 1.3792 \times 10^{-12}\ \text{ GiB/second}$

Therefore, for the Binary system: 1 Kilobit per day ≈ 1.3792 x $10^{-12}$ Gibibytes per second.

Real-World Examples for Other Quantities

10 Kilobits per Day

• Decimal System:
  • $10 \times 1.3477 \times 10^{-12} = 1.3477 \times 10^{-11}$ Gibibytes per second
• Binary System:
  • $10 \times 1.3792 \times 10^{-12} = 1.3792 \times 10^{-11}$ Gibibytes per second

100 Kilobits per Day

• Decimal System:
  • $100 \times 1.3477 \times 10^{-12} = 1.3477 \times 10^{-10}$ Gibibytes per second
• Binary System:
  • $100 \times 1.3792 \times 10^{-12} = 1.3792 \times 10^{-10}$ Gibibytes per second

1 Megabit per Day (1,000 Kilobits)

• Decimal System:
  • $1,000 \times 1.3477 \times 10^{-12} = 1.3477 \times 10^{-9}$ Gibibytes per second
• Binary System:
  • $1,000 \times 1.3792 \times 10^{-12} = 1.3792 \times 10^{-9}$ Gibibytes per second

These conversions help when determining data transfer rates over extended periods, especially useful in low bandwidth systems such as IoT devices or other long-term data logging systems.