bits per hour to Gibibytes per second conversion

How to convert bits per hour to gibibytes per second?

To convert 1 bit per hour (bph) to Gibibytes per second (GiB/s), you need to follow several conversion steps:

1. Convert bits to bytes: 1 byte = 8 bits Therefore, $1 \text{ bit} = \frac{1}{8} \text{ bytes}$.

2. Convert hours to seconds: 1 hour = 3600 seconds Therefore, $1 \text{ bits per hour} = \frac{1}{3600} \text{ bits per second (bps)}$.

3. Combine conversions: $\frac{1 \text{ bit}}{3600 \text{ seconds}} \times \frac{1 \text{ byte}}{8 \text{ bits}} = \frac{1}{28800} \text{ bytes per second (Bps)}$.

4. Convert bytes to gibibytes:

   • For base 2 (binary): 1 GiB = $2^{30}$ bytes = 1,073,741,824 bytes Therefore, $\frac{1}{28800} \text{ Bps} = \frac{1}{28800} \times \frac{1}{1,073,741,824} \text{ GiB/s}$.

   • For base 10: 1 GB (gigabyte) = $10^9$ bytes = 1,000,000,000 bytes Gibibytes (base 2) are actually rarely used in decimal/based 10 calculation, but for practical uniformity in conversions between decimal and binary, the binary/IEC units will predominantly suffice for accuracy. Here is the calculation for completeness: $\frac{1}{28800} \times \frac{1}{1,000,000,000} \text{ GiB/s}$.

Now, let's compute this:

• Base 2 (Binary): $\frac{1}{28800} \times \frac{1}{1,073,741,824} \approx 3.25520833 \times 10^{-14} \text{ GiB/s}$.

• Base 10 (Decimal): $\frac{1}{28800} \times \frac{1}{1,000,000,000} \approx 3.47222222 \times 10^{-14} \text{ GiB/s}$.

Both are quite small values. Now let's present these:

• 1 bit per hour ≈ 3.25520833 × 10^-14 GiB/s (Base 2)
• 1 bit per hour ≈ 3.47222222 × 10^-14 GiB/s (Base 10)

Real-World Examples for Different Quantities

If instead you have higher rates of bits per hour, let's extend these conversions for more real-world practicalities:

• 10 bits per hour:

  • Base 2: $3.25520833 \times 10^{-13} \text{ GiB/s}$.
  • Base 10: $3.47222222 \times 10^{-13} \text{ GiB/s}$.

• 1,000,000 bits per hour (1 megabit per hour):

  • Base 2: $3.25520833 \times 10^{-8} \text{ GiB/s}$.
  • Base 10: $3.47222222 \times 10^{-8} \text{ GiB/s}$.

• 100,000,000 bits per hour (100 megabits per hour):

  • Base 2: $3.25520833 \times 10^{-6} \text{ GiB/s}$.
  • Base 10: $3.47222222 \times 10^{-6} \text{ GiB/s}$.

Real-World Context

• Data Transfer for Small IoT Devices:

  • If small IoT sensor devices send 1,000,000 bits per hour, they transmit about $3.25520833 \times 10^{-8}$ GiB per second.

• Streaming Quality Over Time:

  • Streaming services typically use megabits per second (Mbps). If 100Mbps equates to about 360,000,000,000 bits per hour, the conversion to GiB/s helps evaluate and dimension data storage needs.

These practical examples show the link between data transfer rates in bits per hour and Gibibytes per second, illustrating the impact of small to large data streams in real-world digital communication and storage systems.