bits per hour to Mebibits per second conversion

How to convert bits per hour to mebibits per second?

Sure, let's break down the conversion from bits per hour to Mebibits per second and explore the difference between base 10 and base 2 results, along with some real-world examples.

Understanding the Units:

1. Bits per hour (b/h) is a unit that measures data transfer rate per hour.
2. Mebibit (Mibit) is a binary-based data size unit where 1 Mibit = 2^20 bits.

Conversion Steps:

1. Convert bits per hour to bits per second (b/s):

   • There are 3600 seconds in an hour.
   • Therefore, to convert from bits per hour to bits per second: $\text{bits per second} = \frac{\text{bits per hour}}{3600}$

2. Convert bits per second to Mebibits per second:

   • In base 2 (binary system), 1 Mibit = 2^20 bits. $\text{Mebibits per second (base 2)} = \frac{\text{bits per second}}{2^{20}}$

Calculation:

1. Convert 1 bit per hour to bits per second: $\text{bits per second} = \frac{1 \text{ bit per hour}}{3600 \text{ seconds per hour}} = 2.77778 \times 10^{-4} \text{ bits per second}$

2. Convert bits per second to Mebibits per second (Base 2): $\text{Mebibits per second (base 2)} = \frac{2.77778 \times 10^{-4} \text{ bits per second}}{2^{20}} \approx 2.647 \times 10^{-10} \text{ Mibits per second}$

So, 1 bit per hour is approximately $2.647 \times 10^{-10} \text{ Mibits per second}$ (base 2).

Real-World Examples for Other Quantities of Bits per Hour:

1. 56 Kbit/h:

   • Common speed in early dial-up modems.
   • $\text{bits per second} = \frac{56000}{3600} \approx 15.56 \text{ b/s}$
   • $\text{Mebibits per second} = \frac{15.56}{2^{20}} \approx 1.485 \times 10^{-5} \text{ Mibits per second}$

2. 10 Gbit/h (10 billion bits per hour):

   • Comparable to high-speed network transfer over several hours.
   • $\text{bits per second} = \frac{10 \times 10^9}{3600} \approx 2.777 \times 10^6 \text{ b/s}$
   • $\text{Mebibits per second} = \frac{2.777 \times 10^6}{2^{20}} \approx 2.647 \text{ Mibits per second}$

Base 10 (Decimal System) Comparison:

• In base 10, Mebibits per second would still use the same conversion from b/h to b/s: $\text{Megabits per second (base 10)} = \frac{2.77778 \times 10^{-4} \text{ bits per second}}{10^6} = 2.77778 \times 10^{-10} \text{ Megabits per second}$
• The slight difference is due to the varying definition of the prefix "Mega" in base 10 (which is 10^6) versus base 2 (which is 2^20).

So,

• $1 \text{ bit per hour} = 2.647 \times 10^{-10} \text{ Mibits per second}$ (base 2)
• $1 \text{ bit per hour} = 2.77778 \times 10^{-10} \text{ Megabits per second}$ (base 10)

The difference is subtle but distinct when dealing with binary (base 2) and decimal (base 10) interpretations of data transfer rates.