Megabits per day to Gibibytes per second conversion

How to convert megabits per day to gibibytes per second?

Converting data transfer rates from megabits per day to gibibytes per second involves several steps due to the difference in time units and the need to understand how many bits are in a gibibyte. Let's go through this process carefully.

Definitions:

1. Megabit (Mb): $1 \text{ Megabit} = 1,000,000 \text{ bits}$ (base 10)
2. Gibibyte (GiB): $1 \text{ Gibibyte} = 2^{30} \text{ bytes} = 1,073,741,824 \text{ bytes}$ (base 2)
3. Bit: A single unit of digital data.
4. Byte: 8 bits.

Steps to convert:

1. Convert megabits to bits: $1 \text{ Megabit} = 1,000,000 \text{ bits}$

2. Convert days to seconds: $1 \text{ day} = 24 \times 60 \times 60 = 86,400 \text{ seconds}$

3. Convert bits to gibibytes:

   • First, understand that $1 \text{ Gibibyte} = 2^{30} \text{ bytes}$
   • Since 1 byte = 8 bits, $1 \text{ Gibibyte} = 2^{30} \times 8 = 8,589,934,592 \text{ bits}$

Conversion process:

1. Calculation in base 2:

• Convert 1 megabit per day to bits per second: $\frac{1,000,000 \text{ bits}}{86,400 \text{ seconds}} \approx 11.574 \text{ bits per second}$

• Convert bits per second to gibibytes per second: $\frac{11.574 \text{ bits per second}}{8,589,934,592 \text{ bits per gibibyte}} \approx 1.348 \times 10^{-9} \text{ GiB/s}$

2. Calculation in base 10:

If you're using the base 10 (SI units) approach where 1 GiB = $10^9$ bytes (which is not standard but occasionally used informally for simplicity):

• Convert megabits to bytes (1 byte = 8 bits): $1 \text{ Megabit} = 1,000,000 \text{ bits} \times \frac{1 \text{ byte}}{8 \text{ bits}} = 125,000 \text{ bytes}$

• Bytes per day to bytes per second: $\frac{125,000 \text{ bytes}}{86,400 \text{ seconds}} \approx 1.447685 \text{ bytes per second}$

• Bytes per second to "Gibibytes" per second (for standard SI approach): $\frac{1.447685 \text{ bytes per second}}{1,000,000,000 \text{ bytes (1 GiB-SI)}} \approx 1.447685 \times 10^{-9} \text{ GiB/s (SI)}$

Real-world Examples:

1. Daily Streaming Data:

   • 10 Megabits per day:
     • Base 2: $\approx 1.348 \times 10^{-8} \text{ GiB/s}$
     • Base 10: $\approx 1.447685 \times 10^{-8} \text{ GiB/s (SI)}$

2. Monthly Usage:

   • Let's imagine a low-data IoT sensor uses 1 Megabit per day over a month (30 days):
     • Total data per month: $30 \times 1 \text{ Megabit/day} = 30 \text{ Megabits}$
     • In base 2: $\approx 30 \times 1.348 \times 10^{-9} \text{ GiB/s} = 4.044 \times 10^{-8} \text{ GiB/s}$
     • In base 10: $\approx 30 \times 1.447685 \times 10^{-9} \text{ GiB/s} = 4.343055 \times 10^{-8} \text{ GiB/s (SI)}$

3. Frequent Data Reporting:

   • If a weather station reports 50 Megabits per day:
     • Base 2: $\approx 50 \times 1.348 \times 10^{-9} \text{ GiB/s} = 6.74 \times 10^{-8} \text{ GiB/s}$
     • Base 10: $\approx 50 \times 1.447685 \times 10^{-9} \text{ GiB/s (SI)} = 7.238425 \times 10^{-8} \text{ GiB/s (SI)}$

By understanding these conversions, you can accurately gauge the data transfer rates and storage requirements for various applications.