bits per day to Mebibytes per second conversion

How to convert bits per day to mebibytes per second?

Certainly! Converting bits per day to Mebibytes per second involves a few steps, since these two units measure data rates at different scales. Both base 10 (decimal) and base 2 (binary) conversions can be slightly tricky, so let’s break them down.

Base 10 (Decimal) Calculation:

1. Identify the Units: 1 bit/day and Mebibytes/sec (MiB/s)

2. Convert Days to Seconds: 1 day = 24 hours = 24 × 60 minutes = 24 × 60 × 60 seconds = 86,400 seconds.

3. Convert Bits to Bytes:

   • In base 10: 1 Mebibyte (MB) = 1,000,000 bytes.
   • Therefore, 1 bit = $\frac{1}{8}$ bytes.

4. Calculate Bits per Second (bps):

   • $\text{bps} = \frac{1 \text{ bit}}{86,400 \text{ seconds}}$.

5. Convert Bits per Second to Mebibytes per Second:

   • Base 10: $\text{MBps} = bps \times \frac{1}{8,000,000}$.
   • Thus, $\text{MBps} = \frac{1}{86,400 \times 8,000,000}$.

   Now compute: $\text{MBps} = 1.449 \times 10^{-12} \text{ MBps} \approx 1.45 \times 10^{-12} \text{ MBps}$.

Base 2 (Binary) Calculation:

1. Identify the Units: 1 bit/day and Mebibytes/sec (MiB/s), where 1 Mebibyte = 2^20 bytes.

2. Convert Days to Seconds:

   • 1 day = 24 hours = 24 × 60 minutes = 24 × 60 × 60 seconds = 86,400 seconds.

3. Convert Bits to Bytes:

   • In base 2: 1 byte = 8 bits.
   • Therefore, 1 bit = $\frac{1}{8}$ bytes.

4. Calculate Bits per Second (bps):

   • $\text{bps} = \frac{1 \text{ bit}}{86,400 \text{ seconds}}$.

5. Convert Bits per Second to Mebibytes per Second:

   • Base 2: $\text{MiBps} = bps \times \frac{1}{8 \times 2^{20}}$.
   • So, $\text{MiBps} = \frac{1}{86,400 \times 8 \times 1,048,576}$.

   Now compute: $\text{MiBps} = 1.455 \times 10^{-12} \text{ MiBps} \approx 1.46 \times 10^{-12} \text{ MiBps}$.

Summarized Results:

• Base 10 (Decimal): 1 bit/day ≈ 1.45 x 10^{-12} MBps.
• Base 2 (Binary): 1 bit/day ≈ 1.46 x 10^{-12} MiBps.

These values are extraordinarily small, indicating that data transferred at this rate is virtually negligible.

Real-World Examples with Different Quantities:

1. 100 bits/day:

   • Base 10: 1.58 x 10^{-10} MBps.
   • Base 2: 1.67 x 10^{-10} MiBps.

2. 1 Kilobit (1,000 bits)/day:

   • Base 10: 1.45 x 10^{-9} MBps.
   • Base 2: 1.46 x 10^{-9} MiBps.

3. 1 Megabit (1,000,000 bits)/day:

   • Base 10: 1.45 x 10^{-6} MBps.
   • Base 2: 1.46 x 10^{-6} MiBps.

Such low data rates are mainly for academic or highly specialized low-bandwidth applications like long-term sensor data collection, certain telemetry data, or ultra-low-speed data communications in remote areas.