Gibibits per day to Mebibits per second conversion

How to convert gibibits per day to mebibits per second?

To convert from Gibibits per day (Gib/day) to Mebibits per second (Mib/s), we need to understand the relationship between these units and then consider the time conversion from days to seconds.

Understanding the Units

• Gibibit (Gib): A Gibibit is $2^{30}$ bits.
• Mebibit (Mib): A Mebibit is $2^{20}$ bits.
• Day: A day is 24 hours, with each hour having 60 minutes, and each minute having 60 seconds. Thus, a day is $24 \times 60 \times 60 = 86,400$ seconds.

Conversion Steps

1. Convert Gibibits to Mebibits:

   • $1$ Gib = $2^{30}$ bits
   • $1$ Mib = $2^{20}$ bits
   • Therefore, $1$ Gib = $\frac{2^{30}}{2^{20}}$ Mib = $2^{10}$ Mib = 1024 Mib

2. Convert days to seconds:

   • 1 day = 86,400 seconds

3. Convert Gibibits per day to Mebibits per second:

   • $1$ Gib/day = $1024$ Mib/day
   • Since there are 86,400 seconds in a day: $\frac{1024 \, \text{Mib}}{86,400 \, \text{s}} = \frac{1024}{86,400} \, \text{Mib/s} \approx 0.01185 \, \text{Mib/s}$

Base 10 vs Base 2

• Base 2 (Binary): The above calculation uses base 2 (binary) since Gibibits and Mebibits are binary-based units.

• Base 10 (Decimal): If using standard decimal units (Gigabits and Megabits), the calculation changes:

  • 1 Gigabit (Gb) = $10^9$ bits
  • 1 Megabit (Mb) = $10^6$ bits
  • $1 \, \text{Gb/day} = \frac{10^9 \, \text{bits} / \text{day}}{10^6 \, \text{bits}/\text{Mb}}$

  Using the same time conversion:

  $= \frac{1000\, \text{Mb}}{86,400 \, \text{s}} \approx 0.01157 \, \text{Mb/s}$

Real World Examples

Here are some conversions of different amounts of Gibibits per day to Mebibits per second:

1. 10 Gib/day:

   • $10 \times 1024 \, \text{Mib/day} = 10,240 \, \text{Mib/day}$
   • $\frac{10,240 \, \text{Mib}}{86,400 \, \text{s}} \approx 0.1185 \, \text{Mib/s}$

2. 50 Gib/day:

   • $50 \times 1024 \, \text{Mib/day} = 51,200 \, \text{Mib/day}$
   • $\frac{51,200 \, \text{Mib}}{86,400 \, \text{s}} \approx 0.5926 \, \text{Mib/s}$

3. 100 Gib/day:

   • $100 \times 1024 \, \text{Mib/day} = 102,400 \, \text{Mib/day}$
   • $\frac{102,400 \, \text{Mib}}{86,400 \, \text{s}} \approx 1.185 \, \text{Mib/s}$

These examples give a sense of how different transfer rates convert when switching units and considering time.