bits per second to Megabits per day conversion

How to convert bits per second to megabits per day?

To convert from bits per second (bps) to megabits per day, you need to understand how many seconds are in a day and how many bits are in a megabit. Let's break down the conversion for both base 10 (decimal) and base 2 (binary) systems.

Base 10 (Decimal) Conversion

In the decimal system, 1 megabit (Mb) = 1,000,000 bits (b).

1. Determine the number of seconds in a day: $1 \text{ day} = 24 \text{ hours} \times 60 \text{ minutes/hour} \times 60 \text{ seconds/minute} = 86,400 \text{ seconds}$

2. Calculate bits per day: $1 \text{ bits/second} \times 86,400 \text{ seconds/day} = 86,400 \text{ bits/day}$

3. Convert bits per day to megabits per day: $86,400 \text{ bits/day} \div 1,000,000 \text{ bits/megabit} = 0.0864 \text{ megabits/day}$

Base 2 (Binary) Conversion

In the binary system, 1 megabit (Mb) = $2^{20}$ bits = 1,048,576 bits.

1. Determine the number of seconds in a day: $1 \text{ day} = 24 \text{ hours} \times 60 \text{ minutes/hour} \times 60 \text{ seconds/minute} = 86,400 \text{ seconds}$

2. Calculate bits per day: $1 \text{ bits/second} \times 86,400 \text{ seconds/day} = 86,400 \text{ bits/day}$

3. Convert bits per day to megabits per day: $86,400 \text{ bits/day} \div 1,048,576 \text{ bits/megabit} \approx 0.0824 \text{ megabits/day}$

Thus:

• In the decimal system: 0.0864 megabits/day
• In the binary system: 0.0824 megabits/day

Real-World Examples of Bits per Second

1. Slow Dial-Up Internet:

   • Speed: 56 kbps (kilobits per second)
   • Base 10 conversion: $56,000 \text{ bits/second} \times 86,400 \text{ seconds/day} \div 1,000,000 \approx 4.8384 \text{ megabits/day}$

2. Standard Home Broadband:

   • Speed: 50 Mbps (megabits per second)
   • Base 10 conversion: $50,000,000 \text{ bits/second} \times 86,400 \text{ seconds/day} \div 1,000,000 \approx 4,320,000 \text{ megabits/day} = 4320 \text{ gigabits/day}$

3. High-Speed Fiber Optic Internet:

   • Speed: 1 Gbps (gigabit per second)
   • Base 10 conversion: $1,000,000,000 \text{ bits/second} \times 86,400 \text{ seconds/day} \div 1,000,000 \approx 86,400,000 \text{ megabits/day} = 86,400 \text{ gigabits/day}$

Summary Table:

Speed	Bits/Second	Megabits/Day (Base 10)	Megabits/Day (Base 2)
1 bps	1	0.0864	0.0824
56 kbps	56,000	4.8384	4.6108
50 Mbps	50,000,000	4320	4119.1406
1 Gbps	1,000,000,000	86,400	82,350.5859

This table highlights the difference in the calculations for base 10 and base 2 systems when converting data transfer rates into daily measures.