Kibibits per day to Gibibits per second conversion

How to convert kibibits per day to gibibits per second?

Sure! Let's start by understanding the conversions.

Definitions:

• Kibibit (Kibit): A unit of data equal to $2^{10}$ (1024) bits.
• Gibibit (Gibit): A unit of data equal to $2^{30}$ (1,073,741,824) bits.
• Day: A period of 24 hours (or $86400$ seconds).

To convert $1$ Kibibit per day ($1$ Kibit/day) to Gibibits per second ($Gibit/s$), you need to follow these steps:

Base 2 Conversion:

1. Convert Days to Seconds: $1 \text{ day} = 86400 \text{ seconds}$

2. Convert Kibibits to Gibibits: $1 \text{ Kibibit} = 1024 \text{ bits}$ $1 \text{ Gibibit} = 2^{30} \text{ bits} = 1073741824 \text{ bits}$

3. Calculate Bits per Second (bps): $1 \text{ Kibit/day} = \frac{1024 \text{ bits}}{86400 \text{ seconds}} \text{ bps}$

4. Convert Bits per Second to Gibibits per Second: $\frac{1024 \text{ bits}}{86400 \text{ seconds}} \times \frac{1 \text{ Gibit}}{1073741824 \text{ bits}} = \frac{1024}{86400 \times 1073741824} \text{ Gibit/s}$

   Simplifying this: $\frac{1024}{86400 \cdot 1073741824} = \frac{1}{90720000000}$

   Therefore: $1 \text{ Kibit/day} = 1.1 \times 10^{-11} \text{ Gibit/s}$

Base 10 Conversion (Using Decimal System):

1. Kibibit in Base 10 Conversion: $1 \text{ Kibibit} = 1000 \text{ bits}$ $1 \text{ Gibibit} = 10^9 \text{ bits} = 1000000000 \text{ bits}$

2. Calculate Bits per Second (bps): $1 \text{ Kibit/day} = \frac{1000 \text{ bits}}{86400 \text{ seconds}} \text{ bps}$

3. Convert Bits per Second to Gibibits per Second: $\frac{1000 \text{ bits}}{86400 \text{ seconds}} \times \frac{1 \text{ Gibit}}{1000000000 \text{ bits}} = \frac{1000}{86400 \times 1000000000} \text{ Gibit/s}$

   Simplifying this: $\frac{1000}{86400 \cdot 1000000000} = \frac{1}{86400000000}$

   Therefore: $1 \text{ Kibit/day} = 1.16 \times 10^{-11} \text{ Gibit/s}$

Real-World Examples for Other Quantities of Kibibits per Day:

1. 10 Kibibits/day: $10 \text{ Kibit/day} = 1.1 \times 10^{-10} \text{ Gibit/s (base 2)}$ $10 \text{ Kibit/day} = 1.16 \times 10^{-10} \text{ Gibit/s (base 10)}$

2. 1000 Kibibits/day: $1000 \text{ Kibit/day} = 1.1 \times 10^{-8} \text{ Gibit/s (base 2)}$ $1000 \text{ Kibit/day} = 1.16 \times 10^{-8} \text{ Gibit/s (base 10)}$

3. 1 Megabit/day (1 Mbit/day) (Using base 2): $1 \text{ Mbit} = 1024 \text{ Kibit}$ $\text{Therefore, } 1 \text{ Mb/day} = 1024 \times 1.1 \times 10^{-11} \text{ Gibit/s (base 2 only)}$ $1\text{ Mb/day} = 1.1 \times 10^{-8} \text{ Gibit/s}$

In practical applications, the differences between base 2 and base 10 may matter significantly, especially for storage and communication technologies.