bits per second to Mebibits per month conversion

How to convert bits per second to mebibits per month?

To convert 1 bit per second (bps) to Mebibits per month (Mi/month), we need to account for both the amount of time in a month and the difference between binary and decimal unit conventions.

Step-by-Step Conversion

1. Time in Seconds per Month:

To find the number of seconds in a month, we use an average:

• Assume 30.44 days per month (since it's the average length of a month).
• There are 24 hours in a day, 60 minutes in an hour, and 60 seconds in a minute.

So, total seconds in a month: $30.44 \text{ days/month} \times 24 \text{ hours/day} \times 60 \text{ minutes/hour} \times 60 \text{ seconds/minute} = 2,629,824 \text{ seconds/month}$

2. Convert Bits to Mebibits (Base 2):

In the binary (base-2) system, 1 Mebibit (Mi) = $2^{20}$ bits = 1,048,576 bits.

So, to convert 1 bps to Mebibits per month: $\frac{1 \text{ bps} \times 2,629,824 \text{ seconds/month}}{1,048,576 \text{ bits/Mi}} = \frac{2,629,824 \text{ bits/month}}{1,048,576 \text{ bits/Mi}} \approx 2.51 \text{ Mi/month}$

3. Convert Bits to Megabits (Base 10):

In the decimal (base-10) system, 1 Megabit (Mb) = $10^6$ bits = 1,000,000 bits.

So, to convert 1 bps to Megabits per month: $\frac{1 \text{ bps} \times 2,629,824 \text{ seconds/month}}{1,000,000 \text{ bits/Mb}} = \frac{2,629,824 \text{ bits/month}}{1,000,000 \text{ bits/Mb}} = 2.63 \text{ Mb/month}$

Summary:

• 1 bit per second is approximately 2.51 Mebibits per month (using base-2 units).
• 1 bit per second is approximately 2.63 Megabits per month (using base-10 units).

Real-World Examples

1. 56 kbps Dial-Up Internet Connection:

   • Base 2: 56 kbps = $56 \times 2.51 \approx 140.56$ Mi/month.
   • Base 10: 56 kbps = $56 \times 2.63 \approx 147.28$ Mb/month.

2. 1 Mbps Broadband Connection:

   • Base 2: 1 Mbps = $1000 \times 2.51 \approx 2510$ Mi/month.
   • Base 10: 1 Mbps = $1000 \times 2.63 \approx 2630$ Mb/month.

3. 5 Gbps High-Speed Internet:

   • Base 2: 5 Gbps = $5000000 \times 2.51 \approx 12,550,000$ Mi/month.
   • Base 10: 5 Gbps = $5000000 \times 2.63 \approx 13,150,000$ Mb/month.

These examples show how much data can be transferred over a variety of internet connection speeds in a month, both using binary and decimal unit conventions.