Mebibits per hour to Gibibytes per second conversion

How to convert mebibits per hour to gibibytes per second?

To convert 1 Mebibit per hour (Mebi/hour) to Gibibytes per second (Gibi/second), you need to follow a series of conversion steps. Both binary (base 2) and decimal (base 10) conversions will be demonstrated.

Base 2 Conversion (Binary):

1 Mebibit (Mebi) = $2^{20}$ bits = 1,048,576 bits

1 Gibibyte (Gibi) = $2^{30}$ bytes = 1,073,741,824 bytes

Since 1 byte = 8 bits: 1 Gibibyte in bits = $1,073,741,824 \times 8 = 8,589,934,592$ bits

Now let's convert 1 Mebibit per hour to Gibibytes per second:

Step 1: Convert Mebibits to bits $1 \text{ Mebibit} = 1,048,576 \text{ bits}$

Step 2: Convert hours to seconds $1 \text{ hour} = 3600 \text{ seconds}$

Step 3: Calculate bits per second (bps) from Mebibits per hour $1 \text{ Mebibit/hour} = \frac{1,048,576 \text{ bits}}{3600 \text{ seconds}} \approx 291.27 \text{ bits/second}$

Step 4: Convert bits per second to Gibibytes per second $1 \text{ Gibibyte} = 8,589,934,592 \text{ bits}$ $1 \text{ bit} = \frac{1}{8,589,934,592} \text{ Gibibytes}$

So, $1 \text{ bit/second} = \frac{1}{8,589,934,592} \text{ Gibibytes/second}$ $291.27 \text{ bits/second} \times \frac{1}{8,589,934,592} \text{ Gibibytes/second} \approx 3.39 \times 10^{-8} \text{ Gibibytes/second}$

Base 10 Conversion (Decimal):

For the base 10 conversion, we use standard SI units where: 1 Megabit (Mb) = $10^6$ bits 1 Gigabyte (GB) = $10^9$ bytes = $8 \times 10^9$ bits

Step 1: Convert Mebibits to bits $1 \text{ Mebibit} = 1,048,576 \text{ bits}$ (use the same Mebibit definition since it is always base 2)

Step 2: Convert hours to seconds $1 \text{ hour} = 3600 \text{ seconds}$

Step 3: Calculate bits per second (bps) from Mebibits per hour $1 \text{ Mebibit/hour} = \frac{1,048,576 \text{ bits}}{3600 \text{ seconds}} \approx 291.27 \text{ bits/second}$

Step 4: Convert bits per second to Gigabytes per second $1 \text{ Gigabyte} = 8 \times 10^9 \text{ bits}$ $1 \text{ bit} = \frac{1}{8 \times 10^9} \text{ Gigabytes}$

So, $1 \text{ bit/second} = \frac{1}{8 \times 10^9} \text{ Gigabytes/second}$ $291.27 \text{ bits/second} \times \frac{1}{8 \times 10^9} \text{ Gigabytes/second} \approx 3.64 \times 10^{-8} \text{ Gigabytes/second}$

Real-World Examples for Different Mebibits per hour

1. Streaming Low-Quality Audio (~2 Mebi/hour):

   • Equivalent to $2 \times 291.27 = 582.54$ bits/second, which is approximately $6.78 \times 10^{-8}$ Gibibytes/second (base 2).

2. Downloading a modest size software update (500 Mebi/hour):

   • This would be $500 \times 291.27 = 145,635$ bits/second, or around $1.69 \times 10^{-5}$ Gibibytes/second (base 2).

3. High-definition Video Streaming (~2 GiB/hour):

   • Since 1 GiB is approximately 1024 Mebi, 2 GiB/hour would be approximately 2048 Mebi/hour.
   • This translates to $2048 \times 291.27 \approx 596,725.76$ bits/second or about $6.95 \times 10^{-5}$ Gibibytes/second (base 2).

By using these conversions and examples, you can get a sense of different data rates depending on the context.