Bytes per second to Gibibits per hour conversion

How to convert bytes per second to gibibits per hour?

To convert Bytes per second (B/s) to Gibibits per hour (Gibibits/h), we'll need to understand the following:

1. Bytes per second (B/s) to Bits per second (b/s):

   • 1 Byte = 8 bits
   • Therefore, 1 B/s = 8 b/s.

2. Bits per second (b/s) to Gibibits per second (Gibibits/s):

   • 1 Gibibit = $2^{30}$ bits (base 2).
   • Therefore, 1 Gibibit/s = $2^{30}$ bits/s.

3. Bits per second (b/s) to Gibibits per hour (Gibibits/h):

   • There are 3600 seconds in an hour.
   • Therefore, to convert bits per second to bits per hour, multiply by 3600.

Now we'll combine everything for base 2:

Calculation for Base 2:

1. Convert 1 B/s to bits per second: $1 \text{ B/s} = 8 \text{ b/s}$

2. Convert bits per second to bits per hour: $8 \text{ b/s} \times 3600 \text{ s/hr} = 28800 \text{ b/hr}$

3. Convert bits per hour to Gibibits per hour: $\frac{28800 \text{ b/hr}}{2^{30} \text{ b/Gib}} = \frac{28800}{1073741824}\text{ Gibibits/hr} \approx 2.68 \times 10^{-5} \text{ Gibibits/hr}$

Calculation for Base 10:

In base 10, Gibibits are sometimes approximated with Gigabits using the SI definition, where:

1. 1 Gigabit = $10^9$ bits (base 10).
2. 1 Gibibit = $2^{30}$ bits (as calculated above), but for base 10, we use Gigabit (10^9 bits).

Using the same procedure and converting 1 B/s to Gigibits/h:

1. Convert 1 B/s to bits per second: $1 B/s = 8 \text{ b/s}$

2. Convert bits per second to bits per hour: $8 \text{ b/s} \times 3600 \text{ s/hr} = 28800 \text{ b/hr}$

3. Convert bits per hour to Gigibits per hour: $\frac{28800 \text{ b/hr}}{10^9 \text{ b/Gb}} = \frac{28800}{10^9}\text{ Gigibits/hr} = 2.88 \times 10^{-5} \text{ Gigibits/hr}$

Real-World Examples of Data Transfer Rates:

To better understand various rates of data transfer, here are some real-world examples:

1. 56K Modem: 56 Kbps:

   • 56 Kilobits per second = 56,000 bits per second.
   • 56,000 b/s ≈ 6.7 Kilobytes per second (since 1 Byte = 8 bits).

2. Broadband Internet: 100 Mbps (Megabits per second):

   • 100 Megabits per second = 100,000,000 bits per second.
   • 100,000,000 b/s = 12.5 Megabytes per second.

3. USB 3.0: 5 Gbps (Gigabits per second):

   • 5 Gigabits per second = 5,000,000,000 bits per second.
   • 5,000,000,000 b/s = 625 Megabytes per second.

4. Fiber Internet: 1 Gbps (Gigabit per second):

   • 1 Gigabit per second = 1,000,000,000 bits per second.
   • 1,000,000,000 b/s = 125 Megabytes per second.

In practice, when dealing with networking and data transfer scenarios, it's important to know which base (base 10 vs. base 2) the context is using, as this can drive significant differences in calculations, similar to the differences illustrated in the original conversion you requested.