bits per minute to Gibibytes per second conversion

How to convert bits per minute to gibibytes per second?

To convert bits per minute (bpm) to gibibytes per second (GiB/s), you need to follow a step-by-step conversion process.

1. Convert bits per minute to bits per second: There are 60 seconds in a minute, so you divide the bits per minute by 60 to get bits per second (bps).

2. Convert bits to bytes: There are 8 bits in a byte, so you divide the bps by 8 to get bytes per second (Bps).

3. Convert bytes to gibibytes: This step depends on whether you're using base 2 or base 10.

Base 10 (Decimal System)

In the decimal system, 1 gigabyte (GB) is defined as $10^9$ bytes.

• 1 gibibyte (GiB) in base 10 is $2^{30}$ bytes (which is 1,073,741,824 bytes).

Base 2 (Binary System)

In the binary system, 1 gibibyte (GiB) is 1024^3 bytes.

• 1 gibibyte (GiB) in base 2 is $1024^3$ bytes (which is the same 1,073,741,824 bytes).

Conversion from bits per minute to gibibytes per second:

1. Convert bits per minute to bits per second: $1 \text{ bits per minute} \div 60 \text{ seconds/minute} = \frac{1}{60} \text{ bits per second} \approx 0.0167 \text{ bits per second}$

2. Convert bits per second to bytes per second: $0.0167 \text{ bits per second} \div 8 \text{ bits/byte} = 0.002083 \text{ bytes per second}$

3. Convert bytes per second to gibibytes per second (using base 2): $0.002083 \text{ bytes per second} \div 1,073,741,824 \text{ bytes/GiB} \approx 1.94 \times 10^{-12} \text{ GiB per second}$

The conversion to gibibytes per second would be the same for both base 2 and base 10, as 1 GiB is equal to 1,073,741,824 bytes in both systems. Thus:

$1 \text{ bits per minute} = 1.94 \times 10^{-12} \text{ GiB per second}$

Real-world examples for other quantities of bits per minute:

• 56 kbps dial-up modem: $56,000 \text{ bits/min} \div 60 = 933.33 \text{ bits/second}$

• T1 line (1.544 Mbps): $1,544,000 \text{ bits/min} \div 60 = 25,733.33 \text{ bits/second}$

• Fiber optic network (1 Gbps): $1,000,000,000 \text{ bits/min} \div 60 = 16,666,666.67 \text{ bits/second}$

• Wi-Fi 6 (9.6 Gbps): $9,600,000,000 \text{ bits/min} \div 60 = 160,000,000 \text{ bits/second}$

These examples illustrate how bits per minute can be scaled to represent common data transfer rates in real-world networking scenarios.