bits per day to Megabits per second conversion

How to convert bits per day to megabits per second?

To convert bits per day (b/day) to Megabits per second (Mbps), you'll need to perform a series of unit conversions. Here's how you can do it:

1. Convert bits per day to bits per second (bps).
2. Convert bits per second to Megabits per second (Mbps).

Let's go step-by-step.

Step 1: 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. So, the number of seconds in one day is: $1 \text{ day} = 24 \times 60 \times 60 = 86,400 \text{ seconds}$

Therefore, to convert bits per day to bits per second: $\text{bps} = \frac{\text{b/day}}{86,400 \text{ seconds/day}}$

Step 2: Convert Bits per Second to Megabits per Second

1 Megabit (Mb) = 1,000,000 bits (using base 10). 1 Megabit (Mib) = 1,048,576 bits (2¹⁰ x 2²⁰) (using base 2).

So, to convert bits per second to Megabits per second (base 10): $\text{Mbps} = \frac{\text{bps}}{1,000,000}$

And for base 2: $\text{Mibps} = \frac{\text{bps}}{1,048,576}$

Now, let's do the conversion for 1 bit per day:

Base 10 Conversion:

1. First, convert 1 bit per day to bits per second: $\text{bps} = \frac{1 \text{ bit/day}}{86,400 \text{ seconds/day}} \approx 1.157 \times 10^{-5} \text{ bps}$

2. Then, convert bits per second to Megabits per second (base 10): $\text{Mbps} = \frac{1.157 \times 10^{-5} \text{ bps}}{1,000,000} \approx 1.157 \times 10^{-11} \text{ Mbps}$

Base 2 Conversion:

1. First, convert 1 bit per day to bits per second: $\text{bps} = \frac{1 \text{ bit/day}}{86,400 \text{ seconds/day}} \approx 1.157 \times 10^{-5} \text{ bps}$

2. Then, convert bits per second to Megabits per second (base 2): $\text{Mibps} = \frac{1.157 \times 10^{-5} \text{ bps}}{1,048,576} \approx 1.104 \times 10^{-11} \text{ Mibps}$

Real World Examples:

• 10,000 bits per day:

  • Base 10: $\approx 1.157 \times 10^{-7} \text{ Mbps}$
  • Base 2: $\approx 1.104 \times 10^{-7} \text{ Mibps}$

• 1,000,000 bits per day:

  • Base 10: $\approx 1.157 \times 10^{-5} \text{ Mbps}$
  • Base 2: $\approx 1.104 \times 10^{-5} \text{ Mibps}$

• 86,400,000 bits per day (which is 1 bps):

  • Base 10: $\approx 0.0864 \text{ Mbps}$
  • Base 2: $\approx 0.0824 \text{ Mibps}$

These examples illustrate how various quantities of data transfer measured in bits per day can be converted into more practical units like Megabits per second.