bits per second to Terabytes per minute conversion

How to convert bits per second to terabytes per minute?

Sure, let's walk through the conversion process from bits per second (bps) to terabytes per minute (TB/min). We'll cover both base 10 (decimal system) and base 2 (binary system) approaches, as there is a difference between them.

1. Base 10 (Decimal System)

In the decimal system, the prefixes are based on powers of 10.

1 byte = 8 bits 1 kilobyte (kB) = 1,000 bytes 1 megabyte (MB) = 1,000 kilobytes (kB) 1 gigabyte (GB) = 1,000 megabytes (MB) 1 terabyte (TB) = 1,000 gigabytes (GB)

Conversion Steps:

1. Convert bits to bytes: 1 bit = 1/8 bytes

2. Convert seconds to minutes: 1 second = 1/60 minutes

3. Calculate 1 bit per second in terms of terabytes per minute: $1 \text{ bps} = \frac{1 \text{ bit}}{\text{second}} \times \frac{1 \text{ byte}}{8 \text{ bits}} \times \frac{1 \text{ kilobyte}}{1,000 \text{ bytes}} \times \frac{1 \text{ megabyte}}{1,000 \text{ kilobytes}} \times \frac{1 \text{ gigabyte}}{1,000 \text{ megabytes}} \times \frac{1 \text{ terabyte}}{1,000 \text{ gigabytes}} \times \frac{60 \text{ seconds}}{1 \text{ minute}}$

4. Simplifying, we get: $1 \text{ bit per second} = \frac{60}{8 \times 1,000^4} \text{ terabytes per minute}$

5. Calculation: $1 \text{ bps} = \frac{60}{8 \times 10^{12}} \text{ TB/min}$ $1 \text{ bps} = \frac{60}{8,000,000,000,000} \text{ TB/min}$ $1 \text{ bps} ≈ 7.5 \times 10^{-12} \text{ TB/min}$

2. Base 2 (Binary System)

In the binary system, the prefixes are based on powers of 2.

1 byte = 8 bits 1 kibibyte (KiB) = 1,024 bytes 1 mebibyte (MiB) = 1,024 kibibytes (KiB) 1 gibibyte (GiB) = 1,024 mebibytes (MiB) 1 tebibyte (TiB) = 1,024 gibibytes (GiB)

Conversion Steps:

1. Convert bits to bytes: 1 bit = 1/8 bytes

2. Convert seconds to minutes: 1 second = 1/60 minutes

3. Calculate 1 bit per second in terms of tebibytes per minute: $1 \text{ bps} = \frac{1 \text{ bit}}{\text{second}} \times \frac{1 \text{ byte}}{8 \text{ bits}} \times \frac{1 \text{ kibibyte}}{1,024 \text{ bytes}} \times \frac{1 \text{ mebibyte}}{1,024 \text{ kibibytes}} \times \frac{1 \text{ gibibyte}}{1,024 \text{ mebibytes}} \times \frac{1 \text{ tebibyte}}{1,024 \text{ gibibytes}} \times \frac{60 \text{ seconds}}{1 \text{ minute}}$

4. Simplifying, we get: $1 \text{ bit per second} = \frac{60}{8 \times 1,024^4} \text{ tebibytes per minute}$

5. Calculation: $1 \text{ bps} = \frac{60}{8 \times 1,073,741,824} \text{ TiB/min}$ $1 \text{ bps} = \frac{60}{8,796,093,022,208} \text{ TiB/min}$ $1 \text{ bps} ≈ 6.84 \times 10^{-12} \text{ TiB/min}$

Real World Examples

1. 1 Megabit per Second (1 Mbps)

   • Base 10: $1 \text{ Mbps} = 10^6 \text{ bps}$ $1 \text{ Mbps} ≈ 7.5 \times 10^{-6} \text{ TB/min}$
   • Base 2: $1 \text{ Mbps} = 1,048,576 \text{ bps}$ $1 \text{ Mbps} ≈ 6.84 \times 10^{-6} \text{ TiB/min}$

2. 100 Megabits per Second (100 Mbps)

   • Base 10: $100 \text{ Mbps} ≈ 7.5 \times 10^{-4} \text{ TB/min}$
   • Base 2: $100 \text{ Mbps} ≈ 6.84 \times 10^{-4} \text{ TiB/min}$

3. 1 Gigabit per Second (1 Gbps)

   • Base 10: $1 \text{ Gbps} ≈ 7.5 \times 10^{-3} \text{ TB/min}$
   • Base 2: $1 \text{ Gbps} ≈ 6.84 \times 10^{-3} \text{ TiB/min}$

These calculations help illustrate the conversion differences between the two bases and provide examples of how different data transfer rates translate into terabytes per minute in both systems.