Gibibytes per day to Mebibits per second conversion

How to convert gibibytes per day to mebibits per second?

To convert 1 Gibibyte per day (GiB/day) to Mebibits per second (Mibps), you need to understand the relationships between these units.

Base 2 (Binary System)

• 1 Gibibyte (GiB) = 2^30 bytes = 1,073,741,824 bytes
• 1 byte = 8 bits
• 1 Mebibit (Mib) = 2^20 bits = 1,048,576 bits

Let's break down the conversion step-by-step:

1. Determine the number of bytes in 1 Gibibyte: $1 \text{ GiB} = 1,073,741,824 \text{ bytes}$

2. Convert bytes to bits: $1,073,741,824 \text{ bytes} \times 8 = 8,589,934,592 \text{ bits}$

3. Convert bits to Mebibits: $8,589,934,592 \text{ bits} \div 1,048,576 = 8192 \text{ Mib}$

4. Determine the number of seconds in a day: $1 \text{ day} = 24 \text{ hours} \times 60 \text{ minutes} \times 60 \text{ seconds} = 86,400 \text{ seconds}$

5. Calculate the rate in Mebibits per second: $8192 \text{ Mib} \div 86,400 \text{ seconds} \approx 0.0948 \text{ Mibps}$

Base 10 (Decimal System)

While data transfer rates are typically measured in the binary system, we'll go through the same process using SI (base 10) units for theoretical purposes.

• 1 Gibibyte (GiB) in the binary system is different from the decimal system, but for simplicity, using similar conversions:
• 1 Gigabyte (GB) in base 10 = 10^9 bytes = 1,000,000,000 bytes
• 1 byte = 8 bits
• 1 Megabit (Mb) = 10^6 bits = 1,000,000 bits

Repeat similar steps for conversion in base 10:

1. Determine the number of bytes in 1 Gigabyte: $1 \text{ GB} = 1,000,000,000 \text{ bytes}$

2. Convert bytes to bits: $1,000,000,000 \text{ bytes} \times 8 = 8,000,000,000 \text{ bits}$

3. Convert bits to Megabits: $8,000,000,000 \text{ bits} \div 1,000,000 = 8000 \text{ Mb}$

4. Calculate the rate in Megabits per second: $8000 \text{ Mb} \div 86,400 \text{ seconds} \approx 0.0926 \text{ Mbps}$

Real World Examples for Other Quantities of Gibibytes per Day

1. 10 GiB/day: $10 \text{ GiB/day} \approx 0.948 \text{ Mibps} \text{ (Binary)}$

2. 100 GiB/day: $100 \text{ GiB/day} \approx 9.48 \text{ Mibps} \text{ (Binary)}$

3. 1 TiB/day (1 TiB = 1024 GiB): $1024 \text{ GiB/day} \approx 97.3 \text{ Mibps} \text{ (Binary)}$

These conversions can be useful in various real-world scenarios such as estimating the required bandwidth for cloud storage, data backup systems, or streaming large volumes of data.