Kilobits per second to Gibibits per day conversion

How to convert kilobits per second to gibibits per day?

Sure, let's break down the process of converting 1 Kilobit per second to Gibibits per day, and examine both base 10 and base 2 conversions.

Base 10 Conversion

1. Understanding the units:

   • 1 Kilobit (Kb) = 1,000 bits, as per base 10.

2. Convert Kilobits per second to bits per second:

   • 1 Kb/s = 1,000 bits per second (b/s).

3. Convert bits per second to bits per day: $1,000 \text{ b/s} \times 60 \text{ seconds/minute} \times 60 \text{ minutes/hour} \times 24 \text{ hours/day} = 86,400,000 \text{ bits/day}.$

4. Convert bits per day to Gibibits per day:

   • 1 Gibibit = 1 Gi = $10^9$ bits in base 10.

   $\frac{86,400,000 \text{ bits/day}}{10^9 \text{ bits/Gibibit}} = 0.0864 \text{ Gibibits/day}.$

Base 2 Conversion

1. Understanding the units:

   • 1 Kilobit (Kb) = $2^{10}$ bits in base 2, which equals 1,024 bits.

2. Convert Kilobits per second to bits per second:

   • 1 Kb/s = 1,024 bits per second (b/s).

3. Convert bits per second to bits per day: $1,024 \text{ b/s} \times 60 \text{ seconds/minute} \times 60 \text{ minutes/hour} \times 24 \text{ hours/day} = 88,473,600 \text{ bits/day}.$

4. Convert bits per day to Gibibits per day:

   • 1 Gibibit = 1 Gi = $2^{30}$ bits in base 2, which equals 1,073,741,824 bits.

   $\frac{88,473,600 \text{ bits/day}}{1,073,741,824 \text{ bits/Gibibit}} \approx 0.0824 \text{ Gibibits/day}.$

Summary

• Base 10: $0.0864 \text{ Gibibits/day}$
• Base 2: $0.0824 \text{ Gibibits/day}$

Real-World Examples for Other Quantities of Kilobits per Second

1. Streaming Audio:

   • A basic streaming audio service may use 128 Kb/s.
   • Base 10: $128 \times 0.0864 \text{ Gibibits/day} = 11.0592 \text{ Gibibits/day}$.
   • Base 2: $128 \times 0.0824 \text{ Gibibits/day} = 10.5472 \text{ Gibibits/day}$.

2. Standard Definition (SD) Video Streaming:

   • SD video may use around 1,500 Kb/s.
   • Base 10: $1,500 \times 0.0864 \text{ Gibibits/day} = 129.6 \text{ Gibibits/day}$.
   • Base 2: $1,500 \times 0.0824 \text{ Gibibits/day} = 123.6 \text{ Gibibits/day}$.

3. High-Speed Internet Connection:

   • A high-speed internet package might offer 100,000 Kb/s (100 Mb/s).
   • Base 10: $100,000 \times 0.0864 \text{ Gibibits/day} = 8,640 \text{ Gibibits/day}$.
   • Base 2: $100,000 \times 0.0824 \text{ Gibibits/day} = 8,240 \text{ Gibibits/day}$.