Megabytes per second to Mebibits per hour conversion

How to convert megabytes per second to mebibits per hour?

Certainly! To convert 1 Megabyte per second (MBps) to Mebibits per hour (Mibits/hr), we need to take into account the differences between base 10 and base 2 units of measurement.

Base 10 Conversion

1 Megabyte per second (MBps) in base 10 is:

• 1 MB = 1,000,000 bytes
• 1 byte = 8 bits
• So, 1 MB = 8,000,000 bits

Therefore:

• 1 MBps = 8,000,000 bits per second (bps)

To find out how many bits per hour this is:

• There are 60 seconds in a minute and 60 minutes in an hour, so there are 3600 seconds in an hour.
• So, $8,000,000 \text{ bps} \times 3600 \text{ seconds/hour} = 28,800,000,000 \text{ bits/hour}$

To convert bits to Mebibits, we use the base 2 conversion for a Mebibit:

• 1 Mebibit (Mibit) = 2^20 bits = 1,048,576 bits

Thus, the conversion:

• $28,800,000,000 \text{ bits/hour} \div 1,048,576 \text{ bits/Mibit} \approx 27,450.56 \text{ Mibits/hour}$

Base 2 Conversion

Base 2 defines a Megabyte a bit differently, where:

• 1 Megabyte (MB) = 2^20 bytes = 1,048,576 bytes
• 1 byte = 8 bits
• So, 1 Megabyte (MB) = 8,388,608 bits

Therefore:

• 1 MBps in base 2 = 8,388,608 bits per second (bps)

To find out how many bits per hour:

• $8,388,608 \text{ bps} \times 3600 \text{ seconds/hour} = 30,199,948,800 \text{ bits/hour}$

To convert bits to Mebibits:

• $30,199,948,800 \text{ bits/hour} \div 1,048,576 \text{ bits/Mibit} \approx 28,800 \text{ Mibits/hour}$

Real-World Examples for Other Quantities of MBps

1. Streaming 4K Video:

   • An uncompressed 4K stream is about 375 MBps. In base 10, that would be $375 \times 8,000,000 = 3,000,000,000 \text{ bps}$.
   • Base 10 to Mibits/hr: $3,000,000,000 \text{ bps} \times 3600 \div 1,048,576 \approx 10,313,412 \text{ Mibits/hr}$.
   • Base 2 to Mibits/hr: $375 \times 8,388,608 \text{ bps} \times 3600 \div 1,048,576 \approx 10,800,000 \text{ Mibits/hr}$.

2. Downloading a 25 GB Game:

   • Suppose you are downloading at 50 MBps.
   • Base 10 to Mibits/hr: $50 \times 8,000,000 \times 3600 \div 1,048,576 \approx 1,372,800 \text{ Mibits/hr}$.
   • Base 2 to Mibits/hr: $50 \times 8,388,608 \times 3600 \div 1,048,576 \approx 1,440,000 \text{ Mibits/hr}$.

These examples illustrate the differences in data capacity and rate when using base 10 versus base 2 systems. The choice between the two depends on the context and the standards being adhered to in particular specifications.