Kibibytes per hour to Gigabytes per second conversion

How to convert kibibytes per hour to gigabytes per second?

To convert 1 Kibibyte per hour (KiB/h) to Gigabytes per second (GB/s), you first need to understand the different units involved and the conversion factors between them.

Understanding the Units:

• 1 Kibibyte (KiB) = 2^10 Bytes = 1024 Bytes
• 1 Kilobyte (KB) = 10^3 Bytes = 1000 Bytes
• 1 Gigabyte (GB) in base 2 (binary) = 2^30 Bytes = 1024^3 Bytes
• 1 Gigabyte (GB) in base 10 (decimal) = 10^9 Bytes = 1000^3 Bytes
• 1 hour = 3600 seconds

Base 2 Conversion:

Using binary (base 2) conversion:

1. Convert Kibibytes (KiB) to Bytes: $1 \text{ KiB} = 1024 \text{ Bytes}$

2. Compute Bytes per second: $1 \text{ KiB/h} = \frac{1024 \text{ Bytes}}{3600 \text{ seconds}} \approx 0.2844 \text{ Bytes/second}$

3. Convert Bytes to Gigabytes in base 2: $1 \text{ GiB} = 2^{30} \text{ Bytes} = 1,073,741,824 \text{ Bytes}$

4. Convert Bytes per second to Gigabytes per second: $0.2844 \text{ Bytes/second} = \frac{0.2844}{1,073,741,824} \text{ GiB/second} \approx 2.65 \times 10^{-10} \text{ GiB/second}$

Base 10 Conversion:

Using decimal (base 10) conversion:

1. Convert Kibibytes to Bytes: $1 \text{ KiB} = 1024 \text{ Bytes}$

2. Compute Bytes per second: $1 \text{ KiB/h} = \frac{1024 \text{ Bytes}}{3600 \text{ seconds}} \approx 0.2844 \text{ Bytes/second}$

3. Convert Bytes to Gigabytes in base 10: $1 \text{ GB} = 10^9 \text{ Bytes} = 1,000,000,000 \text{ Bytes}$

4. Convert Bytes per second to Gigabytes per second: $0.2844 \text{ Bytes/second} = \frac{0.2844}{1,000,000,000} \text{ GB/second} \approx 2.844 \times 10^{-10} \text{ GB/second}$

Real World Examples:

Data Transfer Rates:

1. 5 KiB/h:

   • Base 2: $5 \times 2.65 \times 10^{-10} \text{ GiB/s} \approx 1.33 \times 10^{-9} \text{ GiB/s}$
   • Base 10: $5 \times 2.844 \times 10^{-10} \text{ GB/s} = 1.422 \times 10^{-9} \text{ GB/s}$

2. 10 MiB/h ($10 \times 2^{20} \text{ Bytes/h}$):

   • Base 2:
     • Convert MiB to Bytes: $10 \times 2^{20} = 10,485,760 \text{ Bytes}$
     • Compute Bytes per second: $\frac{10,485,760}{3600} \approx 2913.8 \text{ Bytes/second}$
     • Convert to GiB/s: $2913.8 \text{ Bytes/second} \approx 2.71 \times 10^{-6} \text{ GiB/s}$
   • Base 10:
     • Convert MiB to Bytes: $10 \times 10^6 = 10,000,000 \text{ Bytes}$
     • Compute Bytes per second: $\frac{10,000,000}{3600} \approx 2777.8 \text{ Bytes/second}$
     • Convert to GB/s: $2777.8 \text{ Bytes/second} \approx 2.78 \times 10^{-6} \text{ GB/s}$

3. 100 GiB/h:

   • Base 2:
     • Convert GiB to Bytes: $100 \times 2^{30} = 100 \times 1,073,741,824 = 107,374,182,400 \text{ Bytes}$
     • Compute Bytes per second: $\frac{107,374,182,400}{3600} \approx 29,826,162 \text{ Bytes/second}$
     • Convert to GiB/s: $\frac{29,826,162}{1,073,741,824} \approx 0.0278 \text{ GiB/s}$
   • Base 10:
     • Convert GiB to Bytes (since GiB in decimal is ambiguous, use similar conversion as GB):
       • Base 10, transform GiB into bytes if taken as GB operation for easier understanding,
       • $100 \times 10^9 \text{ Bytes} = 100 \times 1,000,000,000 = 100,000,000,000 \text{ Bytes}$
     • Compute Bytes per second: $\frac{100,000,000,000}{3600} \approx 27,777,777.8 \text{ Bytes/second}$
     • Convert to GB/s: $\frac{27,777,777.8}{1,000,000,000} \approx 0.0278 \text{ GB/s}$

These conversions help illustrate the different scales and necessary steps for accurately converting between these units.