Kibibytes per second to Kilobits per hour conversion

How to convert kibibytes per second to kilobits per hour?

Sure, let's go through the conversion process step by step for both base 2 and base 10.

Base 2 (Binary Conversion)

1 Kibibyte (KiB) = 1024 bytes 1 byte = 8 bits 1 KiB = 1024 * 8 bits = 8192 bits

1 Kibibyte per second (KiB/s) = 8192 bits per second (b/s)

To convert to bits per hour: $8192 \text{ b/s} \times 3600 \text{ seconds/hour} = 29491200 \text{ bits/hour}$

To convert bits to Kilobits (Kb): 1 Kilobit (Kb) = 1024 bits (in base 2)

So, $29491200 \text{ bits/hour} \div 1024 \text{ bits/Kb} = 28800 \text{ Kb/hour}$

Base 10 (Decimal Conversion)

1 Kilobyte (KB) in base 10 is defined as 1000 bytes. 1 byte = 8 bits 1 KB = 1000 * 8 bits = 8000 bits

1 Kilobyte per second (KB/s) = 8000 bits per second (b/s)

To convert to bits per hour: $8000 \text{ b/s} \times 3600 \text{ seconds/hour} = 28800000 \text{ bits/hour}$

To convert bits to Kilobits (Kb): 1 Kilobit (Kb) = 1000 bits (in base 10)

So, $28800000 \text{ bits/hour} \div 1000 \text{ bits/Kb} = 28800 \text{ Kb/hour}$

Summary:

• Base 2 (Binary): $1 \text{ KiB/s} = 28800 \text{ Kb/hour}$
• Base 10 (Decimal): $1 \text{ KB/s} = 28800 \text{ Kb/hour}$

In this specific instance, the numerical value in Kilobits per hour happens to be the same for both base 2 and base 10 due to the specific values chosen (1 KiB and 1 KB both converting neatly under these conditions).

Real World Examples for Other Quantities of Kibibytes per Second:

• 5 KiB/s:

  • Base 2: $5 \times 28800 = 144000 \text{ Kb/hour}$
  • Base 10: $5 \times 28800 = 144000 \text{ Kb/hour}$

• 100 KiB/s:

  • Base 2: $100 \times 28800 = 2880000 \text{ Kb/hour}$
  • Base 10: $100 \times 28800 = 2880000 \text{ Kb/hour}$

• 512 KiB/s:

  • Base 2: $512 \times 28800 = 14745600 \text{ Kb/hour}$
  • Base 10: $512 \times 28800 = 14745600 \text{ Kb/hour}$

These conversions and resulting values help illustrate how different rates of data transfer can scale up over time when considering larger periods, such as an hour, and how standardized units simplify these conversions.