Mebibits per hour to Gigabits per second conversion

How to convert mebibits per hour to gigabits per second?

Sure, let's walk through the conversion of 1 Mebibit per hour to Gigabits per second.

Step-by-Step Conversion

Step 1: Convert Mebibits to Bits

1 Mebibit (Mibit) is equivalent to $2^{20}$ bits (since "mebi" is a binary prefix). $1 \text{ Mibit} = 2^{20} \text{ bits} = 1,048,576 \text{ bits}$

Step 2: Convert Hours to Seconds

1 hour is equal to 3,600 seconds. $1 \text{ hour} = 3,600 \text{ seconds}$

Step 3: Calculating Bits per Second

Now, we need to find out how many bits per second are in 1 Mibit per hour. We do this by dividing the total bits by the total seconds. $1 \text{ Mibit per hour} = \frac{1,048,576 \text{ bits}}{3,600 \text{ seconds}} \approx 291.27 \text{ bits per second}$

Step 4: Convert Bits to Gigabits

1 Gigabit (Gbit) is equal to $10^9$ bits (using base 10) or $2^{30}$ bits (using base 2).

Using base 10: $291.27 \text{ bits per second} = 291.27 \times 10^{-9} \text{ Gigabits per second} \approx 0.00000029127 \text{ Gbps}$

Using base 2: $1 \text{ Gigabit (Gbit)} = 2^{30} \text{ bits} = 1,073,741,824 \text{ bits}$ $291.27 \text{ bits per second} = \frac{291.27}{1,073,741,824} \text{ Gbps} \approx 2.71 \times 10^{-7} \text{ Gbps}$

Summary

• Base 10 conversion: $1 \text{ Mibit per hour} \approx 0.00000029127 \text{ Gbps}$
• Base 2 conversion: $1 \text{ Mibit per hour} \approx 2.71 \times 10^{-7} \text{ Gbps}$

Real-World Examples

Now let's consider some real-world equivalents and different magnitudes:

Low-Speed IoT Devices

• 10 Mebibits per hour:
  • Using base 10: $10 \times 0.00000029127 = 0.0000029127 \text{ Gbps}$
  • Using base 2: $10 \times 2.71 \times 10^{-7} = 2.71 \times 10^{-6} \text{ Gbps}$

Home Internet

A standard home internet connection might be rated at Mbps rather than Mibps, but let's make an illustrative comparison.

• 1000 Mebibits per hour:
  • Using base 10: $1000 \times 0.00000029127 = 0.00029127 \text{ Gbps}$
  • Using base 2: $1000 \times 2.71 \times 10^{-7} = 2.71 \times 10^{-4} \text{ Gbps}$

Enterprise Data Centers

High-speed links can carry substantial amounts of data.

• 100,000 Mebibits per hour:
  • Using base 10: $100000 \times 0.00000029127 = 0.029127 \text{ Gbps}$
  • Using base 2: $100000 \times 2.71 \times 10^{-7} = 0.0271 \text{ Gbps}$

These conversions help to understand how data transfer rates given in Mebibits per hour relate to more commonly used metrics like Gigabits per second.