Kilobits per hour to Gibibits per second conversion

How to convert kilobits per hour to gibibits per second?

To convert Kilobits per hour (kb/h) to Gibibits per second (Gib/s), you’ll need to follow these steps:

1. Convert Kilobits to Bits.
2. Convert Hours to Seconds.
3. Convert Bits to Gibibits if needed.

Conversion Factors:

• 1 Kilobit (kb) = 1,000 bits (base 10) or 1,024 bits (base 2).
• 1 Hour = 3,600 seconds.
• 1 Gibibit (Gib) = 1,073,741,824 bits (base 2).

Base 10 Conversion:

1. Convert Kilobits to Bits using base 10: $1 \text{ kb/h} = 1,000 \text{ bits/h}$

2. Convert Hours to Seconds: Since there are 3,600 seconds in an hour, we divide by 3,600 to convert bits per hour to bits per second: $1,000 \text{ bits/h} \times \frac{1 \text{ hour}}{3,600 \text{ seconds}} = 0.27778 \text{ bits/second}$

3. Convert Bits to Gibibits: $0.27778 \text{ bits/second} \times \frac{1 \text{ Gibibit}}{1,073,741,824 \text{ bits}} = 2.587 \times 10^{-10} \text{ Gib/s}$

Base 2 Conversion:

1. Convert Kilobits to Bits using base 2: $1 \text{ kb/h} = 1,024 \text{ bits/h}$

2. Convert Hours to Seconds: Similar to the base 10 conversion, divide by 3,600 to convert bits per hour to bits per second: $1,024 \text{ bits/h} \times \frac{1 \text{ hour}}{3,600 \text{ seconds}} = 0.28444 \text{ bits/second}$

3. Convert Bits to Gibibits: $0.28444 \text{ bits/second} \times \frac{1 \text{ Gibibit}}{1,073,741,824 \text{ bits}} = 2.649 \times 10^{-10} \text{ Gib/s}$

Real World Examples:

• 10,000 Kilobits per hour (base 10):

  • Convert to Bits per second: $10,000 \text{ kb/h} = 10,000,000 \text{ bits/h}$
  • Convert to Bits per second: $10,000,000 \div 3,600 = 2,777.78 \text{ bits/s}$
  • Convert to Gibibits per second: $2,777.78 \div 1,073,741,824 = 2.589 \times 10^{-6} \text{ Gib/s}$

• 500,000 Kilobits per hour (base 2):

  • Convert to Bits per second: $500,000 \times 1,024 = 512,000,000 \text{ bits/h}$
  • Convert to Bits per second: $512,000,000 \div 3,600 = 142,222.22 \text{ bits/s}$
  • Convert to Gibibits per second: $142,222.22 \div 1,073,741,824 = 1.325 \times 10^{-4} \text{ Gib/s}$

These examples illustrate both base 10 and base 2 conversions for different quantities of Kilobits per hour, providing a practical understanding of the differences and applications of each base system.