Gigabits to Kibibits conversion

How to convert gigabits to kibibits?

Sure! Understanding the conversion between gigabits and kibibits requires knowledge of different numeral systems: base 10 (decimal) and base 2 (binary).

Base 10 (Decimal) System

• 1 gigabit (Gb or Gbit) in the base 10 system is equivalent to $10^9$ bits.
• 1 kibibit (Kibit) in the base 10 system is equivalent to $2^{10}$ bits = 1,024 bits.

To convert gigabits to kibibits, you use the following steps:

$1 \text{ Gbit} = 10^9 \text{ bits}$

$\text{Now convert bits to kibibits} = \frac{10^9 \text{ bits}}{2^{10} \text{ bits/Kibit}}$

$= \frac{10^9}{1,024}$

$= 976,562.5 \text{ Kibits}$

Base 2 (Binary) System

• 1 gibibit (Gibibit or Gibit) in the base 2 system is equivalent to $2^{30}$ bits.
• 1 kibibit (Kibibit or Kibit) in the base 2 system is also equivalent to $2^{10}$ bits = 1,024 bits.

To convert gibibits to kibibits, you use the following steps:

$1 \text{ Gibibit} = 2^{30} \text{ bits} = 1,073,741,824 \text{ bits}$

$\text{Now convert bits to kibibits} = \frac{2^{30} \text{ bits}}{2^{10} \text{ bits/Kibit}}$

$= \frac{1,073,741,824 \text{ bits}}{1,024 \text{ bits/Kibit}}$

$= 1,048,576 \text{ Kibits}$

Real-World Examples for Other Quantities of Gigabits:

1. 10 Gigabits:

   • Base 10: $10 \text{Gb}$ equals $\frac{10 \times 10^9 \text{ bits}}{1,024} = 9,765,625\text{ Kibits}$
   • Base 2: $10 \text{Gibibits}$ equals $10 \times 1,048,576 = 10,485,760 \text{ Kibits}$

2. 50 Gigabits:

   • Base 10: $50 \text{Gb}$ equals $\frac{50 \times 10^9 \text{ bits}}{1,024} = 48,828,125 \text{ Kibits}$
   • Base 2: $50 \text{Gibibits}$ equals $50 \times 1,048,576 = 52,428,800 \text{ Kibits}$

3. 100 Gigabits:

   • Base 10: $100 \text{Gb}$ equals $\frac{100 \times 10^9 \text{ bits}}{1,024} = 97,656,250 \text{ Kibits}$
   • Base 2: $100 \text{Gibibits}$ equals $100 \times 1,048,576 = 104,857,600 \text{ Kibits}$

Summary

• In base 10 (decimal), 1 Gigabit is equivalent to approximately 976,562.5 Kibibits.
• In base 2 (binary), 1 Gibibit is equivalent to 1,048,576 Kibibits.

These conversions are useful in different contexts, such as networking, data storage, and computer architecture, where understanding both decimal and binary representations is necessary.