Mebibytes per day to Tebibytes per second conversion

How to convert mebibytes per day to tebibytes per second?

Sure, let's break down the conversion process and explore how to derive the answer for both base 10 (decimal) and base 2 (binary) measurements.

Conversion Factors

1. Understanding Units:

   • 1 Mebibyte (MiB) = $2^{20}$ bytes = 1,048,576 bytes (base 2).
   • 1 Tebibyte (TiB) = $2^{40}$ bytes = 1,099,511,627,776 bytes (base 2).
   • There are 86,400 seconds in a day (24 hours * 60 minutes * 60 seconds).

2. Conversions:

   • To convert Mebibytes per day to Tebibytes per second, we'll need to convert MiB (base 2) to bytes, then bytes to TiB, and then adjust for the time (seconds in a day).

Base 2 Calculation

1. Calculate bytes per day: $1 \text{ MiB/day} = 1 \times 1,048,576 \text{ bytes/day}$

2. Convert bytes per day to bytes per second: $1,048,576 \text{ bytes/day} \div 86,400 \text{ seconds/day} = 12.13888889 \text{ bytes/second}$

3. Convert bytes per second to Tebibytes per second: $12.13888889 \text{ bytes/second} \div 1,099,511,627,776 \text{ bytes/TiB} = 1.104 \times 10^{-11} \text{ TiB/second}$

Base 10 Calculation (Decimal)

1. Understanding Units:

   • 1 Megabyte (MB) = $10^6$ bytes = 1,000,000 bytes (base 10).
   • 1 Terabyte (TB) = $10^{12}$ bytes = 1,000,000,000,000 bytes (base 10).

2. Calculate bytes per day: $1 \text{ MB/day} = 1 \times 1,000,000 \text{ bytes/day}$

3. Convert bytes per day to bytes per second: $1,000,000 \text{ bytes/day} \div 86,400 \text{ seconds/day} = 11.57407407 \text{ bytes/second}$

4. Convert bytes per second to Terabytes per second: $11.57407407 \text{ bytes/second} \div 1,000,000,000,000 \text{ bytes/TB} = 1.157 \times 10^{-11} \text{ TB/second}$

Real World Examples

• 10 MiB/day:

  • Base 2: $10 \times 1.104 \times 10^{-11} \text{ TiB/second} = 1.104 \times 10^{-10} \text{ TiB/second}$
  • Base 10: $10 \times 1.157 \times 10^{-11} \text{ TB/second} = 1.157 \times 10^{-10} \text{ TB/second}$

• 100 MiB/day:

  • Base 2: $100 \times 1.104 \times 10^{-11} \text{ TiB/second} = 1.104 \times 10^{-9} \text{ TiB/second}$
  • Base 10: $100 \times 1.157 \times 10^{-11} \text{ TB/second} = 1.157 \times 10^{-9} \text{ TB/second}$

• 1 GiB/day (1 GiB = 1024 MiB):

  • Base 2: $1024 \times 1.104 \times 10^{-11} \text{ TiB/second} = 1.13 \times 10^{-8} \text{ TiB/second}$
  • Base 10: $1024 \times 1.157 \times 10^{-11} \text{ TB/second} = 1.19 \times 10^{-8} \text{ TB/second}$

Remember that the exact differences between the calculations for base 10 and base 2 can matter a lot in contexts that are sensitive to precise calculations, such as data storage and transfer in computing.