Bytes per day to Mebibits per second conversion

How to convert bytes per day to mebibits per second?

To convert data transfer rates from Bytes per day to Mebibits per second (Mibps), you need to follow a two-step process: convert Bytes per day to Bits per second (bps), and then convert bps to Mebibits per second (Mibps).

Step 1: Convert Bytes per day to Bits per second (bps)

Bytes per day (B/day) can be converted to Bits per second (bps) using the following formula:

$\text{Bits per second (bps)} = \frac{\text{Bytes per day} \times 8}{24 \times 3600}$

• 1 Byte = 8 bits
• 1 day = 24 hours = 24 × 3600 seconds = 86400 seconds

$\text{bps} = \frac{1 \times 8}{86400} = \frac{8}{86400} = 9.259 \times 10^{-5} \text{bps}$

Step 2: Convert Bits per second to Mebibits per second (Mibps)

1 Mebibit = $2^{20}$ bits = 1,048,576 bits

$\text{Mibps} = \frac{\text{bps}}{2^{20}}$

So,

$\text{Mibps} = \frac{9.259 \times 10^{-5} \text{bps}}{1,048,576}$

$\text{Mibps} = 8.834 \times 10^{-11} \text{Mibps}$

Difference for Base 10 and Base 2

In the context of the base-2 (binary) system commonly used in computing, we already made our conversion. It is not typical to convert to Mibps using the decimal (base-10) system since Mibps inherently uses binary measurement.

However, for thoroughness, if we were to use Megabits per second with the base-10 (decimal) system (Mbps, where 1 Megabit = $10^6$ bits), the conversion would be slightly different:

$\text{Mbps} = \frac{\text{bps}}{10^6}$

$\text{Mbps} = \frac{9.259 \times 10^{-5} \text{bps}}{10^6}$

$\text{Mbps} = 9.259 \times 10^{-11} \text{Mbps}$

Real-World Examples

Consider more practical data rates scaled up for real-world scenarios:

1. 1 Megabyte per day (1 MB/day) to Mibps:

   • 1 Megabyte = $1,000,000$ Bytes (base-10) or $1,048,576$ Bytes (base-2).
   • Calculate bits per second: $\text{bps} = \frac{1,048,576 \times 8}{86400} \approx 97.66 \text{bps}$
   • Convert bps to Mibps: $\text{Mibps} = \frac{97.66}{1,048,576} \approx 9.32 \times 10^{-5} \text{Mibps}$

2. 1 Gigabyte per day (1 GB/day) to Mibps:

   • 1 Gigabyte = $1,000,000,000$ Bytes (base-10) or $1,073,741,824$ Bytes (base-2).
   • Calculate bits per second: $\text{bps} = \frac{1,073,741,824 \times 8}{86400} \approx 99,168.6 \text{bps}$
   • Convert bps to Mibps: $\text{Mibps} = \frac{99,168.6}{1,048,576} \approx 0.0946 \text{Mibps}$

3. 1 Terabyte per day (1 TB/day) to Mibps:

   • 1 Terabyte = $1,000,000,000,000$ Bytes (base-10) or $1,099,511,627,776$ Bytes (base-2).
   • Calculate bits per second: $\text{bps} = \frac{1,099,511,627,776 \times 8}{86400} \approx 101,536,655.48 \text{bps}$
   • Convert bps to Mibps: $\text{Mibps} = \frac{101,536,655.48}{1,048,576} \approx 96.85 \text{Mibps}$