Kilobits per hour to Gibibytes per day conversion

How to convert kilobits per hour to gibibytes per day?

To convert 1 kilobit per hour (kb/h) to gibibytes per day (GiB/day), we need to go through a couple of conversion steps. Use the binary base for Gibibytes (as it is a binary unit) but also demonstrate how base 10 would be used for comparison if it's required.

Binary Base (Base 2)

1. Convert kilobits to bits: $1 \text{ kilobit} = 1 \times 10^3 \text{ bits} = 1000 \text{ bits}$

2. Convert per hour to per day: $1000 \text{ bits/hour} \times 24 \text{ hours/day} = 24,000 \text{ bits/day}$

3. Convert bits to bytes: $8 \text{ bits} = 1 \text{ byte}$ $24,000 \text{ bits/day} \div 8 = 3000 \text{ bytes/day}$

4. Convert bytes to gibibytes: $1 \text{ gibibyte} = 2^{30} \text{ bytes} = 1,073,741,824 \text{ bytes}$ $\frac{3000 \text{ bytes/day}}{1,073,741,824 \text{ bytes/gibibyte}} \approx 2.7939677 \times 10^{-6} \text{ GiB/day}$

Decimal Base (Base 10)

1. Convert kilobits to bits: $1 \text{ kilobit} = 1 \times 1000 \text{ bits} = 1000 \text{ bits}$

2. Convert per hour to per day: $1000 \text{ bits/hour} \times 24 \text{ hours/day} = 24,000 \text{ bits/day}$

3. Convert bits to bytes: $8 \text{ bits} = 1 \text{ byte}$ $24,000 \text{ bits/day} \div 8 = 3000 \text{ bytes/day}$

4. Convert bytes to gigabytes (decimal): $1 \text{ gigabyte} = 10^9 \text{ bytes} = 1,000,000,000 \text{ bytes}$ $\frac{3000 \text{ bytes/day}}{1,000,000,000 \text{ bytes/gigabyte}} = 3 \times 10^{-6} \text{ GB/day}$

Real World Examples

Now, let's apply these conversions to some practical scenarios:

1. Medium-Speed Home Internet:

   • Consider a speed of 1000 kilobits per hour (which is 1 megabit/hour).
   • Converting using the above method, we get: $24,000,000 \text{ bits/day} / 8 = 3,000,000 \text{ bytes/day}$ $3,000,000 \text{ bytes/day} / 1,073,741,824 \approx 0.00279 \text{ GiB/day}$
     • In Base 10: Approximately 0.003 GB/day.

2. Slow Mobile Data Usage:

   • Consider a speed of 50 kilobits per hour.
   • Converting using the same method: $1,200,000 \text{ bits/day} / 8 = 150,000 \text{ bytes/day}$ $150,000 \text{ bytes/day} / 1,073,741,824 \approx 0.00014 \text{ GiB/day}$
     • In Base 10: Approximately 0.00015 GB/day.

3. High Capacity Download Server:

   • Consider a speed of 100,000 kilobits per hour.
   • Converting using the same method: $2,400,000,000 \text{ bits/day} / 8 = 300,000,000 \text{ bytes/day}$ $300,000,000 \text{ bytes/day} / 1,073,741,824 \approx 0.279 \text{ GiB/day}$
     • In Base 10: Approximately 0.3 GB/day.

These are practical examples that showcase different internet speeds or data transfer scenarios and how they would convert to GiB/day or GB/day using both binary and decimal bases.