bits per second to Megabytes per minute conversion

How to convert bits per second to megabytes per minute?

To convert from bits per second (bps) to megabytes per minute (MB/min), you need to go through several conversion steps. Here’s a structured way to do it:

Conversion Process:

Base 10 (Decimal System)

1. Start with 1 bit per second (bps).
2. Bits to bytes: There are 8 bits in a byte. $\frac{1 \text{ bit}}{\text{second}} \times \frac{1 \text{ byte}}{8 \text{ bits}} = 0.125 \text{ bytes per second}$
3. Bytes to kilobytes (in base 10, 1 kilobyte = 1000 bytes): $0.125 \text{ bytes per second} \div 1000 = 0.000125 \text{ kilobytes per second}$
4. Kilobytes to megabytes (in base 10, 1 megabyte = 1000 kilobytes): $0.000125 \text{ kilobytes per second} \div 1000 = 0.000000125 \text{ megabytes per second}$
5. Seconds to minutes: There are 60 seconds in a minute. $0.000000125 \text{ megabytes per second} \times 60 = 0.0000075 \text{ megabytes per minute (MB/min)}$

So in base 10: $1 \text{ bit per second} = 0.0000075 \text{ Megabytes per minute (MB/min)}$

Base 2 (Binary System)

1. Start with 1 bit per second.
2. Bits to bytes: There are 8 bits in a byte. $\frac{1 \text{ bit}}{\text{second}} \times \frac{1 \text{ byte}}{8 \text{ bits}} = 0.125 \text{ bytes per second}$
3. Bytes to kibibytes (in base 2, 1 kibibyte = 1024 bytes): $0.125 \text{ bytes per second} \div 1024 = 0.0001220703125 \text{ kibibytes per second}$
4. Kibibytes to mebibytes (in base 2, 1 mebibyte = 1024 kibibytes): $0.0001220703125 \text{ kibibytes per second} \div 1024 = 0.00000011920928955078 \text{ mebibytes per second}$
5. Seconds to minutes: There are 60 seconds in a minute. $0.00000011920928955078 \text{ mebibytes per second} \times 60 = 0.000007152557373046875 \text{ mebibytes per minute (MiB/min)}$

So in base 2: $1 \text{ bit per second} = 0.000007152557373046875 \text{ Mebibytes per minute (MiB/min)}$

Real-World Examples:

Base 10:

• 1 Megabit per second (1 Mbps). $1,000,000 \text{ bits per second} = 1,000,000 \div 8 = 125,000 \text{ bytes per second}$ $125,000 \div 1000 = 125 \text{ kilobytes per second}$ $125 \div 1000 = 0.125 \text{ megabytes per second} \times 60 = 7.5 \text{ Megabytes per minute}$

• 100 Megabits per second (100 Mbps). $100,000,000 \text{ bits per second} = 100,000,000 \div 8 = 12,500,000 \text{ bytes per second}$ $12,500,000 \div 1000 = 12500 \text{ kilobytes per second}$ $12,500 \div 1000 = 12.5 \text{ megabytes per second} \times 60 = 750 \text{ Megabytes per minute}$

Base 2:

• 1 Megabit per second (1 Mibps). $1,048,576 \text{ bits per second} = 1,048,576 \div 8 = 131,072 \text{ bytes per second}$ $131,072 \div 1024 = 128 \text{ kibibytes per second}$ $128 \div 1024 = 0.125 \text{ mebibytes per second} \times 60 = 7.5 \text{ MiB/min}$

• 100 Megabits per second (100 Mibps). $104,857,600 \text{ bits per second} = 104,857,600 \div 8 = 13,107,200 \text{ bytes per second}$ $13,107,200 \div 1024 = 12,800 \text{ kibibytes per second}$ $12,800 \div 1024 = 12.5 \text{ mebibytes per second} \times 60 = 750 \text{ MiB/min}$

These calculations show how different rates of data transfer can be interpreted in both base 10 and base 2 systems, and highlight the importance of specifying which base is being used when dealing with digital data.