Kilobits per day to Gibibytes per hour conversion

How to convert kilobits per day to gibibytes per hour?

Certainly! Let's break down the conversion of 1 kilobits per day (kb/day) to gibibytes per hour (GiB/hr).

Step-by-Step Conversion:

1. Start with 1 kilobits per day (kb/day):

   • 1 kilobit (kb) = 1,000 bits (base 10) or 1,024 bits (base 2).

2. Convert kilobits to bits:

   • If using base 10: $1 \text{ kb} = 1,000 \text{ bits}$
   • If using base 2: $1 \text{ kb} = 1,024 \text{ bits}$

3. Convert days to hours:

   • 1 day = 24 hours.

4. Convert bits to bytes:

   • 1 byte = 8 bits.

5. Convert bytes to gibibytes:

   • 1 gibibyte (GiB) = $2^{30}$ bytes = 1,073,741,824 bytes.

Using Base 10:

1. Convert kb to bits: $1 \text{ kb/day} = 1,000 \text{ bits/day}$

2. Convert bits/day to bits/hour: $\frac{1,000 \text{ bits/day}}{24 \text{ hours/day}} = 41.6667 \text{ bits/hour}$

3. Convert bits/hour to bytes/hour: $\frac{41.6667 \text{ bits/hour}}{8 \text{ bits/byte}} = 5.2083 \text{ bytes/hour}$

4. Convert bytes/hour to gibibytes/hour: $\frac{5.2083 \text{ bytes/hour}}{1,073,741,824 \text{ bytes/GiB}} \approx 4.85 \times 10^{-9} \text{ GiB/hour}$

Using Base 2:

1. Convert kb to bits: $1 \text{ kb/day} = 1,024 \text{ bits/day}$

2. Convert bits/day to bits/hour: $\frac{1,024 \text{ bits/day}}{24 \text{ hours/day}} = 42.6667 \text{ bits/hour}$

3. Convert bits/hour to bytes/hour: $\frac{42.6667 \text{ bits/hour}}{8 \text{ bits/byte}} = 5.3333 \text{ bytes/hour}$

4. Convert bytes/hour to gibibytes/hour: $\frac{5.3333 \text{ bytes/hour}}{1,073,741,824 \text{ bytes/GiB}} \approx 4.97 \times 10^{-9} \text{ GiB/hour}$

Summary:

• Using base 10, 1 kb/day = approximately $4.85 \times 10^{-9}$ GiB/hr.
• Using base 2, 1 kb/day = approximately $4.97 \times 10^{-9}$ GiB/hr.

Real World Examples:

1. Internet Data Plans:

   • A low-speed data plan might offer speeds around 40 kilobits per second (kbps) which equates to 3,456,000 kilobits per day.
   • This translates to approximately 17 megabytes per day (MB/day) at around 0.00064 GiB/hour using base 10.

2. IoT Devices:

   • An IoT sensor that transmits data at 10 kb/day is transmitting at extremely low rates.
   • That equates to around $4.85 \times 10^{-8}$ GiB/hr (base 10).

3. Streaming:

   • High-quality HD video streaming often demands around 5 megabits per second (Mbps).
   • Over a day, this results in 432,000,000 kilobits per day, or approximately 4.75 GiB/hr (base 10).

These conversions help in understanding data usage and requirements in practical scenarios.