bits per minute to Gigabits per second conversion

How to convert bits per minute to gigabits per second?

To convert from bits per minute (bpm) to gigabits per second (Gbps), you need to follow these steps:

1. Convert bits per minute to bits per second (bps): Since there are 60 seconds in a minute, you can convert bits per minute to bits per second using the following formula: $1 \text{ bpm} = \frac{1 \text{ bit}}{60 \text{ seconds}} = \frac{1}{60} \text{ bps}$

2. Convert bits per second to gigabits per second: There are $1,000,000,000$ bits in a gigabit (base 10) and $1,073,741,824$ bits in a gigabit (base 2). Use these conversion factors depending on whether you are using the base 10 or base 2 system.

   Base 10: $1 \text{ bps} = \frac{1}{1,000,000,000} \text{ Gbps}$ Therefore, $\frac{1}{60} \text{ bps} = \frac{1}{60 \times 1,000,000,000} \text{ Gbps} = \frac{1}{60,000,000,000} \text{ Gbps} \approx 1.6667 \times 10^{-11} \text{ Gbps}$

   Base 2: $1 \text{ bps} = \frac{1}{1,073,741,824} \text{ Gbps}$ Therefore, $\frac{1}{60} \text{ bps} = \frac{1}{60 \times 1,073,741,824} \text{ Gbps} \approx 1.55252 \times 10^{-11} \text{ Gbps}$

Real-World Examples for Other Quantities of Bits per Minute

1. 56,000 bits per minute (dial-up modem speed):

   • Base 10: $56,000 \text{ bpm} = \frac{56,000}{60} \text{ bps} = 933.33 \text{ bps}$ $933.33 \text{ bps} = \frac{933.33}{1,000,000,000} \text{ Gbps} = 9.3333 \times 10^{-7} \text{ Gbps}$

   • Base 2: $933.33 \text{ bps} = \frac{933.33}{1,073,741,824} \text{ Gbps} \approx 8.691 \times 10^{-7} \text{ Gbps}$

2. 1,200,000 bits per minute (T1 line speed):

   • Base 10: $1,200,000 \text{ bpm} = \frac{1,200,000}{60} \text{ bps} = 20,000 \text{ bps}$ $20,000 \text{ bps} = \frac{20,000}{1,000,000,000} \text{ Gbps} = 2 \times 10^{-5} \text{ Gbps}$

   • Base 2: $20,000 \text{ bps} = \frac{20,000}{1,073,741,824} \text{ Gbps} \approx 1.863 \times 10^{-5} \text{ Gbps}$

3. 1,000,000,000 bits per minute (higher-speed network connection):

   • Base 10: $1,000,000,000 \text{ bpm} = \frac{1,000,000,000}{60} \text{ bps} = 16,666,666.67 \text{ bps}$ $16,666,666.67 \text{ bps} = \frac{16,666,666.67}{1,000,000,000} \text{ Gbps} = 0.016667 \text{ Gbps}$

   • Base 2: $16,666,666.67 \text{ bps} = \frac{16,666,666.67}{1,073,741,824} \text{ Gbps} \approx 0.01552 \text{ Gbps}$

These examples show how you can convert different bit rates from bits per minute to gigabits per second in both base 10 and base 2 systems.