Mebibits per day to Mebibytes per hour conversion

How to convert mebibits per day to mebibytes per hour?

To convert 1 Mebibit per day (Mibit/day) to Mebibytes per hour (MiB/hr), you need to go through a couple of steps involving unit conversions. Here's the process for both base-2 and base-10 systems.

Understanding Units

1 Mebibit (Mibit) = $2^{20}$ bits = 1,048,576 bits (base-2 system).

1 Mebibyte (MiB) = $2^{20}$ bytes = 1,048,576 bytes (base-2 system).

And, 1 byte = 8 bits.

The day to hour conversion is simple: 1 day = 24 hours.

Step-by-Step Conversion

1. Convert 1 Mebibit per day to bits per day:

$1 \text{ Mibit/day} = 1,048,576 \text{ bits/day}$

2. Convert bits per day to bits per hour:

$1,048,576 \text{ bits/day} \div 24 \text{ hours/day} = 43,690.67 \text{ bits/hour}$

3. Convert bits per hour to bytes per hour (since 1 byte = 8 bits):

$43,690.67 \text{ bits/hour} \div 8 = 5,461.33 \text{ bytes/hour}$

4. Convert bytes per hour to Mebibytes per hour:

$5,461.33 \text{ bytes/hour} \div 1,048,576 \text{ bytes/MiB} = 0.00521 \text{ MiB/hour}$

Comparison with Base-10 (for reference):

In base-10 (SI units): 1 Megabit (Mb) = $10^6$ bits = 1,000,000 bits (base-10 system).

1 Megabyte (MB) = $10^6$ bytes = 1,000,000 bytes (base-10 system).

1. Convert 1 Megabit per day to bits per day:

$1 \text{ Mb/day} = 1,000,000 \text{ bits/day}$

2. Convert bits per day to bits per hour:

$1,000,000 \text{ bits/day} \div 24 \text{ hours/day} = 41,666.67 \text{ bits/hour}$

3. Convert bits per hour to bytes per hour (since 1 byte = 8 bits):

$41,666.67 \text{ bits/hour} \div 8 = 5,208.33 \text{ bytes/hour}$

4. Convert bytes per hour to Megabytes per hour:

$5,208.33 \text{ bytes/hour} \div 1,000,000 \text{ bytes/MB} = 0.00521 \text{ MB/hour}$

Real-World Examples:

1. Streaming Services:

   • A standard video stream at 1 Mbps (Megabit per second) would transfer approximately $1 \text{ Mbps} \times 60 \text{ seconds} \times 60 \text{ minutes} \times 24 \text{ hours} = 86,400 \text{ Mbits/day}$.
   • To convert this to Mebibytes per hour, using the same steps as above.

2. Internet Plans:

   • If an internet plan provides a data limit of 100 Mebibits per day: $100 \text{ Mibit/day} \to 100 \text{ Mibit} \times 0.00521 \text{ MiB/hour} = 0.521 \text{ MiB/hour}$

3. File Transfers (Email, Cloud Storage):

   • If you're sending data at a rate of 10 Mebibits per day: $10 \text{ Mibit/day} \to 10 \text{ Mibit} \times 0.00521 \text{ MiB/hour} = 0.0521 \text{ MiB/hour}$

In summary, using the base-2 system: 1 Mebibit per day is approximately 0.00521 Mebibytes per hour. The same conversion in the base-10 system yields the same numerical result in Megabytes per hour due to the straightforward, linear conversion steps.