Megabits per day to Mebibits per second conversion

How to convert megabits per day to mebibits per second?

Sure, let's start by understanding the basic concepts and conversion factors:

Base 10 (Decimal System):

In the metric system (base 10), units use prefixes like Mega (M). One Megabit (Mb) equals $10^6$ bits.

Base 2 (Binary System):

In the binary system (base 2), which is often used in computing, the prefix Mebi (Mi) is used instead. One Mebibit (Mib) equals $2^{20}$ bits, or 1,048,576 bits.

Conversion Steps:

1. Convert Megabits per Day to Bits per Day:

   • 1 Megabit (Mb) = $10^6$ bits (base 10)
   • Therefore, 1 Megabit per Day (Mb/day) = $10^6$ bits/day

2. Convert Bits per Day to Bits per Second:

   • There are 24 hours in a day, 60 minutes in an hour, and 60 seconds in a minute.
   • Hence, 1 day = 24 * 60 * 60 = 86,400 seconds
   • So, Bits per Second (bps) = $\frac{10^6 \text{ bits}}{86,400 \text{ seconds}}$

3. Convert Bits per Second to Mebibits per Second:

   • 1 Mebibit (Mib) = $2^{20}$ bits = 1,048,576 bits (base 2)

Calculations:

Base 10 (Metric System):

• Bits per Second:
  $\frac{10^6}{86,400} = 11.574 \, \text{bps}$

• There is no difference for Megabits in the base 10 system.

Base 2 (Binary System):

• To convert bits per second to Mebibits per Second: $\text{Mibps} = \frac{\text{Bits per Second}}{2^{20}}$

• Therefore, using the earlier result: $\frac{11.574}{2^{20}} = \frac{11.574}{1,048,576} \approx 0.00001103 \, \text{Mibps}$

Summary:

• 1 Megabit per day ≈ 11.574 bits per second (no difference for base 10 as it remains in standard bits).
• 1 Megabit per day ≈ 0.00001103 Mebibits per second (base 2)

Real-world Examples:

Here are a few more examples for context:

10 Megabits per day:

Base 10:

• Bits per Second: $\frac{10 \times 10^6}{86,400} \approx 115.74 \, \text{bps}$

Base 2:

• Mebibits per Second: $\frac{115.74}{1,048,576} \approx 0.0001103 \, \text{Mibps}$

100 Megabits per day:

Base 10:

• Bits per Second: $\frac{100 \times 10^6}{86,400} \approx 1157.41 \, \text{bps}$

Base 2:

• Mebibits per Second: $\frac{1157.41}{1,048,576} \approx 0.001103 \, \text{Mibps}$

Real-world Applications:

1. Residential Internet Plans:

   Assuming an average residential internet plan allows for 10 Megabits per second (Mbps) download speeds, here's a comparison:

   • 10 Megabits per second = $10 \times 86,400 \times 1,000,000$ = 864,000,000,000 bits per day.
   • Such a speed is immensely higher than 10 Megabits per day.

2. File Downloads:

   Downloading a 100 MB file (~800 Megabits) with a connection of 10 Megabits per day translates to approximately:

   • Filesize $= 800 \times 10^6 \, \text{bits}$
   • Duration = $\frac{800 \times 10^6 \, \text{bits}}{11.574 \, \text{bps}} \approx 69,120 \, \text{seconds} \approx 19.2 \, \text{hours}$

So, converting these measurements and understanding the systems helps you see the difference between theoretic data transfer rates and practical applications.