Mebibytes per day to Gibibits per second conversion

How to convert mebibytes per day to gibibits per second?

Sure! To convert 1 Mebibyte per day to Gibibits per second, it’s important to first understand the definitions and conversions in both base 2 (binary) and base 10 (decimal) units.

Base 2 (Binary):

1. Mebibyte (MiB) = $2^{20}$ Bytes = 1,048,576 Bytes.
2. Gibibit (Gib) = $2^{30}$ Bits = 1,073,741,824 Bits.

There are 24 hours in a day, 60 minutes in an hour, and 60 seconds in a minute. Therefore, there are:

$24 \times 60 \times 60 = 86,400 \text{ seconds in a day}$

To convert Mebibytes to Gibibits:

1 MiB is equivalent to $1,048,576 \times 8$ Bits = 8,388,608 Bits. Therefore, 1 Mebibyte per day in bits per day is:

$1 \text{ MiB/day} \times 8,388,608 \text{ bits} = 8,388,608 \text{ bits/day}$

Now, to find the rate in bits per second, divide by the number of seconds in a day:

$\frac{8,388,608 \text{ bits/day}}{86,400 \text{ seconds/day}} \approx 97.11 \text{ bits/second}$

Finally, convert bits per second to Gibibits per second:

$\frac{97.11 \text{ bits/second}}{1,073,741,824 \text{ bits/Gib}} \approx 9.04 \times 10^{-5} \text{ Gib/second}$

Base 10 (Decimal):

1. Megabyte (MB) = $10^6$ Bytes = 1,000,000 Bytes.
2. Gigabit (Gb) = $10^9$ Bits = 1,000,000,000 Bits.

Using the same number of seconds in a day:

$24 \times 60 \times 60 = 86,400 \text{ seconds in a day}$

To convert Megabytes to Gigabits:

1 MB is equivalent to $1,000,000 \times 8$ Bits = 8,000,000 Bits. Therefore, 1 Megabyte per day in bits per day is:

$1 \text{ MB/day} \times 8,000,000 \text{ bits} = 8,000,000 \text{ bits/day}$

Now, to find the rate in bits per second, divide by the number of seconds in a day:

$\frac{8,000,000 \text{ bits/day}}{86,400 \text{ seconds/day}} \approx 92.59 \text{ bits/second}$

Finally, convert bits per second to Gigabits per second:

$\frac{92.59 \text{ bits/second}}{1,000,000,000 \text{ bits/Gb}} \approx 9.26 \times 10^{-5} \text{ Gb/second}$

Summary:

• Base 2 (Binary):
  • 1 Mebibyte per day ≈ 9.04 × 10⁻⁵ Gibibits per second.
• Base 10 (Decimal):
  • 1 Megabyte per day ≈ 9.26 × 10⁻⁵ Gigabits per second.

Real-World Examples for Other Quantities of Mebibytes per Day:

1. 10 MiB/day:

   • Binary: 10 × 9.04 × 10⁻⁵ Gib/s = 9.04 × 10⁻⁴ Gib/s.
   • Decimal: 10 × 9.26 × 10⁻⁵ Gb/s = 9.26 × 10⁻⁴ Gb/s.

2. 100 MiB/day:

   • Binary: 100 × 9.04 × 10⁻⁵ Gib/s = 9.04 × 10⁻³ Gib/s.
   • Decimal: 100 × 9.26 × 10⁻⁵ Gb/s = 9.26 × 10⁻³ Gb/s.

3. 1 GiB/day (1024 MiB/day):

   • Binary: 1024 × 9.04 × 10⁻⁵ Gib/s = 0.0925 Gib/s.
   • Decimal: (1024 Mebibytes approximates to 1.07374 Gigabytes, but if calculated similar to 1024 MiB):
     • 1024 × 9.26 × 10⁻⁵ Gb/s ≈ 0.095 Gib/s.