Mebibytes per day to Gigabits per hour conversion

How to convert mebibytes per day to gigabits per hour?

Sure! Let's walk through the conversion process step-by-step and provide both base-10 (SI units) and base-2 (binary) equivalents when necessary.

Step 1: Definitions

1. Mebibyte (MiB): A binary unit of data equal to $2^{20}$ bytes, or 1,048,576 bytes.
2. Gigabit (Gb): A metric unit of data equal to $10^9$ bits (SI) or $2^{30}$ bits (binary).

Step 2: Convert Mebibytes to Bytes

1 Megabyte (MiB) = 1,048,576 bytes.

Given:

• 1 MiB/day

Step 3: Convert Bytes to Bits

1 byte = 8 bits. Therefore, $1 \text{ MiB/day} = 1,048,576 \text{ bytes/day} \times 8 \frac{\text{bits}}{\text{byte}} = 8,388,608 \text{ bits/day}$

Step 4: Convert Days to Hours

There are 24 hours in a day. $8,388,608 \text{ bits/day} \div 24 \text{ hours/day} = 349,525.3333 \text{ bits/hour}$

Step 5: Convert Bits to Gigabits (Base-10 and Base-2)

Base-10 Conversion 1 Gigabit (SI) = $10^9$ bits. $349,525.3333 \text{ bits/hour} \div 10^9 \text{ bits/Gb} = 3.495253333 \times 10^{-4} \text{ Gb/hour}$

Base-2 Conversion 1 Gigabit (binary) = $2^{30}$ bits, which equals 1,073,741,824 bits. $349,525.3333 \text{ bits/hour} \div 1,073,741,824 \text{ bits/Gb} \approx 3.253818750 \times 10^{-4} \text{ Gb/hour}$

Real-World Examples

1. 10 MiB/day:

   • Base-10: $10 \times 3.495253333 \times 10^{-4}$ Gb/hour = $3.495253333 \times 10^{-3}$ Gb/hour.
   • Base-2: $10 \times 3.253818750 \times 10^{-4}$ Gb/hour = $3.253818750 \times 10^{-3}$ Gb/hour.

2. 100 MiB/day:

   • Base-10: $100 \times 3.495253333 \times 10^{-4}$ Gb/hour = $3.495253333 \times 10^{-2}$ Gb/hour.
   • Base-2: $100 \times 3.253818750 \times 10^{-4}$ Gb/hour = $3.253818750 \times 10^{-2}$ Gb/hour.

3. 1 GiB/day (Gibibyte) (where 1 GiB = 1,024 MiB):

   • Base-10: $1024 \times 3.495253333 \times 10^{-4}$ Gb/hour = $0.3573290667$ Gb/hour.
   • Base-2: $1024 \times 3.253818750 \times 10^{-4}$ Gb/hour = $0.3338240250$ Gb/hour.

Conclusion

The difference in results between the base-10 and base-2 systems of measurements is due to the way units are defined in each system. Base-10 uses multiples of 10, whereas base-2 uses multiples of 2. This difference becomes more pronounced at larger scales of data.