Gigabytes per month to Mebibits per second conversion

How to convert gigabytes per month to mebibits per second?

When converting data transfer rates, it's important to handle units correctly, particularly distinguishing between base 10 (decimal) and base 2 (binary) units.

Conversion Details: 1 Gigabyte (decimal) = 1,000,000,000 bytes 1 Gibibyte (binary) = 1,073,741,824 bytes

1 byte = 8 bits

Steps to Convert 1 Gigabyte per month to Mebibits per second (MiBps):

Base 10 (Decimal)

1. Convert Gigabytes to bytes: $1 \text{ Gigabyte} = 1,000,000,000 \text{ bytes}$
2. Convert bytes to bits: $1,000,000,000 \text{ bytes} \times 8 = 8,000,000,000 \text{ bits}$
3. Convert bytes per month to bits per second. Assuming a month has 30 days for simplicity: $8,000,000,000 \text{ bits} / (30 \times 24 \times 60 \times 60) \approx 3.086 \text{ bits per second}$
4. Convert bits per second to Mebibits per second: $3.086 \text{ bit/second} / (1024 \times 1024) \approx 0.000002944 \text{ MiBps}$

Base 2 (Binary)

1. Convert Gigabytes to Gibibytes if needed, otherwise stick with base 10 for bytes and handle conversion directly.
2. In binary, 1 GiB = 1,073,741,824 bytes.
3. Use the relation 1 byte = 8 bits and calculate as follows: $1,073,741,824 \text{ bytes} × 8 = 8,589,934,592 \text{ bits}$
4. Convert to bits per second: $8,589,934,592 \text{ bits} / (30 \times 24 \times 60 \times 60) \approx 3.311 \text{ bits per second}$
5. Convert to Mebibits per second (MiBps): $3.311 \text{ bit/second} / (1024 \times 1024) \approx 0.000003159 \text{ MiBps}$

Real-world Examples:

1. 10 Gigabytes per month (Decimal) $10 \text{ GB} = 10 \times 8,000,000,000 \text{ bits} = 80,000,000,000 \text{ bits}$ $80,000,000,000 \text{ bits} / (30 \times 24 \times 60 \times 60) \approx 30.86 \text{ bits per second}$

2. 100 Gigabytes per month (Binary) $100 \text{ GB} = 100 \times 8,589,934,592 \text{ bits} = 858,993,459,200 \text{ bits}$ $858,993,459,200 \text{ bits} / (30 \times 24 \times 60 \times 60) \approx 331.1 \text{ bits per second}$

Summary: For 1 Gigabyte per month:

• In base 10: 0.000002944 MiBps
• In base 2: 0.000003159 MiBps

Multiplying these results by larger values, say 100 Gigabytes per month, gives a plausible data transfer rate which may be used for monthly data cap in Internet Service Plans or similar use cases.