Mebibits per hour to Gigabytes per hour conversion

How to convert mebibits per hour to gigabytes per hour?

To convert from Mebibits per hour to Gigabytes per hour, we need to go through a couple of steps as these units measure data quantities in different bases (binary and decimal). Here's the explanation:

Understanding the Units

• Mebibit (Mibit): 1 Mibit = $2^{20}$ bits = 1,048,576 bits (binary-based)
• Gigabyte (GB): Can be interpreted in both base 10 and base 2.
  • In base 10 (decimal-based): 1 GB = $10^9$ bytes
  • In base 2 (binary-based): 1 GiB (Gibibyte) = $2^{30}$ bytes = 1,073,741,824 bytes

Conversion Process

1. Convert Mebibits to Megabits:

   • Since 1 Mebibit (Mibit) is directly equivalent to 1,048,576 bits, converting is just identifying the scale: $1 \text{ Mebibit} = 1.048576 \times 10^6 \text{ bits}$

2. Convert bits to bytes:

   • 1 byte = 8 bits, so $1.048576 \times 10^6 \text{ bits} = \frac{1.048576 \times 10^6}{8} \text{ bytes} = 131,072 \text{ bytes}$

3. Convert bytes to gigabytes:

   • For base 10 (decimal-based):

     • $1 \text{ GB} = 10^9 \text{ bytes}$
     • $131,072 \text{ bytes} \div 10^9 = 0.000131072 \text{ GB}$

   • For base 2 (binary-based):

     • $1 \text{ GiB} = 2^{30} \text{ bytes} = 1,073,741,824 \text{ bytes}$
     • $131,072 \text{ bytes} \div 1,073,741,824 \text{ bytes} = 0.0001220703125 \text{ GiB}$

Summary of Conversion Equivalent:

• 1 Mebibit per hour is approximately 0.000131072 GB per hour in the base 10 system.
• 1 Mebibit per hour is approximately 0.0001220703125 GiB per hour in the base 2 system.

Real-World Examples for Other Quantities:

1. 10 Mebibits per hour:

   • Base 10: $10 \times 0.000131072 = 0.00131072 \text{ GB per hour}$
   • Base 2: $10 \times 0.0001220703125 = 0.001220703125 \text{ GiB per hour}$

2. 100 Mebibits per hour:

   • Base 10: $100 \times 0.000131072 = 0.0131072 \text{ GB per hour}$
   • Base 2: $100 \times 0.0001220703125 = 0.01220703125 \text{ GiB per hour}$

3. 1000 Mebibits per hour:

   • Base 10: $1000 \times 0.000131072 = 0.131072 \text{ GB per hour}$
   • Base 2: $1000 \times 0.0001220703125 = 0.1220703125 \text{ GiB per hour}$

Practical Contexts:

• Streaming Video Content:

  • A high-definition streaming video might use around 5 Mebibits per second (Mbps). Over an hour, this becomes $5 \times 3600 \text{ seconds} = 18,000 \text{ Mebibits per hour}$.
  • Base 10: $18000 \times 0.000131072 = 2.359296 \text{ GB per hour}$
  • Base 2: $18000 \times 0.0001220703125 = 2.197265625 \text{ GiB per hour}$

• Data Backup:

  • Suppose a network backup transfers data at a rate of 500 Mebibits per hour.
  • Base 10: $500 \times 0.000131072 = 0.065536 \text{ GB per hour}$
  • Base 2: $500 \times 0.0001220703125 = 0.06103515625 \text{ GiB per hour}$

This framework helps you understand how to convert between different units of data transfer and to see practical real-world applications.