Megabits per minute to Gigabits per second conversion

How to convert megabits per minute to gigabits per second?

Sure, I can help you with that! To convert 1 Megabit per minute to Gigabits per second, you'll need to understand the difference between base 10 (decimal) and base 2 (binary) calculations. Let's break it down step by step for both bases.

Base 10 (Decimal System)

1 Megabit (Mb) = $10^6$ bits. There are 60 seconds in a minute.

So, to convert 1 Megabit per minute to bits per second: $1 \text{ Megabit per minute} = \frac{10^6 \text{ bits}}{60 \text{ seconds}}$

To convert bits per second to Gigabits per second: 1 Gigabit (Gb) = $10^9$ bits.

Therefore, $\frac{10^6 \text{ bits}}{60 \text{ seconds}} = \frac{10^6}{60} \text{ bits per second} \approx 16666.67 \text{ bits per second}$

Now convert bits per second to Gigabits per second: $\frac{16666.67 \text{ bits per second}}{10^9} \approx 1.6667 \times 10^{-5} \text{ Gigabits per second (Gbps)}$

Base 2 (Binary System)

1 Megabit (Mb) = $2^{20}$ bits = 1,048,576 bits. Again, there are 60 seconds in a minute.

So, to convert 1 Megabit per minute to bits per second: $1 \text{ Megabit per minute} = \frac{2^{20} \text{ bits}}{60 \text{ seconds}} = \frac{1,048,576 \text{ bits}}{60 \text{ seconds}} \approx 17,476.27 \text{ bits per second}$

To convert bits per second to Gigabits per second: 1 Gigabit (Gb) = $2^{30}$ bits = 1,073,741,824 bits.

Therefore, $\frac{17476.27 \text{ bits per second}}{2^{30}} = \frac{17476.27}{1,073,741,824} \approx 1.6263 \times 10^{-5} \text{ Gigabits per second (Gbps)}$

Real-World Examples for Other Quantities

1. 10 Megabits per minute (Base 10) $10 \text{ Megabits per minute} = 10 \times 1.6667 \times 10^{-5} \text{ Gbps} \approx 1.667 \times 10^{-4} \text{ Gbps}$

2. 50 Megabits per minute (Base 2) $50 \text{ Megabits per minute} = 50 \times 1.6263 \times 10^{-5} \text{ Gbps} \approx 8.1315 \times 10^{-4} \text{ Gbps}$

3. 100 Megabits per minute (Base 10) $100 \text{ Megabits per minute} = 100 \times 1.6667 \times 10^{-5} \text{ Gbps} = 1.6667 \times 10^{-3} \text{ Gbps}$

4. 500 Megabits per minute (Base 2) $500 \text{ Megabits per minute} = 500 \times 1.6263 \times 10^{-5} \text{ Gbps} \approx 8.1315 \times 10^{-3} \text{ Gbps}$

These conversions provide you with a clear understanding of how to shift from Megabits per minute to Gigabits per second in both decimal and binary systems, along with real-world example calculations for different data rates.