Mebibits per hour to Gibibytes per hour conversion

How to convert mebibits per hour to gibibytes per hour?

To convert 1 Mebibit per hour (Mibit/hr) to Gibibytes per hour (GiB/hr), we need to understand the relationship between Mebibits and Gibibytes in both base 2 (binary) and base 10 (decimal) systems.

Base 2 (Binary)

1 Mebibit (Mibit) = 2^20 bits 1 Gibibyte (GiB) = 2^30 bytes 1 byte = 8 bits

Therefore: 1 GiB = 2^30 bytes = 2^30 * 8 bits = 2^33 bits

To convert Mebibits to Gibibytes: $1 \text{ Mibit} = 2^{20} \text{ bits}$ $\Rightarrow 1 \text{ Mibit/hour} = \frac{2^{20} \text{ bits}}{2^{33} \text{ bits/byte}}$ $= \frac{1}{2^{13}} \text{ GiB/hour}$ $= \frac{1}{8192} \text{ GiB/hour}$

So, 1 Mebibit per hour is approximately $1.22 \times 10^{-4} \text{ GiB/hour}$.

Base 10 (Decimal)

In base 10, data storage units are often used as follows: 1 Megabit (Mb) = 10^6 bits 1 Gigabyte (GB) = 10^9 bytes 1 byte = 8 bits

Using these conversions: $1 GB = 10^9 bytes = 8 \times 10^9 bits$

To convert Megabits to Gigabytes: $1 \text{ Mb} = 10^6 \text{ bits}$ $\Rightarrow 1 \text{ Mb/hour} = \frac{10^6 \text{ bits}}{8 \times 10^9 \text{ bits/GB}}$ $= \frac{10^6}{8 \times 10^9} \text{ GB/hour}$ $= \frac{1}{8000} \text{ GB/hour}$

So, in base 10, 1 Megabit per hour (assuming the term 'Mebibit' means 'Megabit') is $1.25 \times 10^{-4} \text{ GB/hour}$.

Real-World Examples of Mebibits per Hour

1. Internet Video Streaming:

   • A standard-definition video stream via an online platform might use around 1–2 Mebibits per second. Based on the base 2 system: $1 \text{ Mibit/sec} \times 3600 \text{ sec/hour} = 3600 \text{ Mibits/hour}$ Therefore, the data rate is 3600 Mibits/hour, which is approximately $0.4395 \text{ GiB/hour}$.

2. Downloading Files:

   • Suppose you are downloading a large file at an average rate of 500 Mebibits per hour. $500 \text{ Mibit/hour} \times \frac{1 \text{ GiB}}{8192 \text{ Mibits}} = 0.061 \text{ GiB/hour}$

3. Home Internet Plan:

   • If your internet service claims a data transfer rate of 5 Mibits per second: $5 \text{ Mibit/second} \times 3600 \text{ seconds/hour} = 18000 \text{ Mibit/hour}$ This translates to: $18000 \text{ Mibits/hour} \times \frac{1 \text{ GiB}}{8192 \text{ Mibits}} = 2.197 \text{ GiB/hour}$

These examples illustrate how different data transfer rates in Mebibits per hour can be utilized and converted into Gibibytes per hour for practical scenarios.