bits per day to Mebibits per second conversion

How to convert bits per day to mebibits per second?

Sure, converting bits per day to Mebibits per second requires a few steps. We'll need to take into account the conversion between different units of time and data storage.

Definitions

1. Bits per day (bit/day): The number of bits transferred in one day.
2. Mebibits per second (Mib/s): A unit of data transfer rate equivalent to 2^20 bits per second (base 2). In base 10, a Mib/s is equivalent to 1,048,576 bits per second (bit/s).

Conversion Formula

To convert from bits per day to Mebibits per second, you need the following steps:

1. Convert bits per day to bits per second: $\text{bits per second (bps)} = \frac{\text{bits per day}}{60 \times 60 \times 24}$ There are 24 hours in a day, 60 minutes in an hour, and 60 seconds in a minute.

2. Convert bits per second to Mebibits per second (Mib/s) using: $1 \, \text{Mib/s} = 2^{20} \, \text{bps} = 1,048,576 \, \text{bps}$

Step-by-Step Calculation

1. Convert 1 bit per day to bits per second: $\text{bps} = \frac{1}{60 \times 60 \times 24} = \frac{1}{86,400} \, \text{bps} \approx 1.157 \times 10^{-5} \, \text{bps}$

2. Convert bits per second to Mebibits per second (Mib/s): $\text{Mib/s} = \frac{\text{bps}}{2^{20}} = \frac{1.157 \times 10^{-5}}{1,048,576} \, \text{Mib/s}$ $\text{Mib/s} \approx 1.104 \times 10^{-11} \, \text{Mib/s}$

Mebibits per Second (Base 10 vs Base 2)

In base 2:

• 1 Mib/s = 2^20 bits per second = 1,048,576 bps.

For base 10 (Megabits):

• 1 Mbit/s = 10^6 bits per second = 1,000,000 bps.

The method above uses base 2, which is standard for computing data rates.

Example for Other Quantities of Bits per Day

1. 1,000 bits per day:

   • Convert to bps: $\frac{1000}{86,400} \approx 0.01157 \, \text{bps}$
   • Convert to Mib/s: $\frac{0.01157}{1,048,576} \approx 1.104 \times 10^{-8} \, \text{Mib/s}$

2. 1,000,000 bits per day:

   • Convert to bps: $\frac{1,000,000}{86,400} \approx 11.574 \, \text{bps}$
   • Convert to Mib/s: $\frac{11.574}{1,048,576} \approx 1.104 \times 10^{-5} \, \text{Mib/s}$

3. 1,000,000,000 bits per day (1 Gigabit per day):

   • Convert to bps: $\frac{1,000,000,000}{86,400} \approx 11,574 \, \text{bps}$
   • Convert to Mib/s: $\frac{11,574}{1,048,576} \approx 0.011 \, \text{Mib/s}$

Real-World Examples

• Dial-Up Internet Speed: An old 56 Kbps (56,000 bits per second) connection would be approximately 4,924,800,000 bits per day, so dividing by 86,400 gives about 5694.44 bps. Converting that to Mib/s: $\frac{5694.44}{1,048,576} \approx 0.0054 \, \text{Mib/s}$.

• Modern Broadband: A 100 Mbps (100,000,000 bits per second) connection would transfer approximately $100,000,000 \times 86,400$ bits per day, which converts directly to 100 Mbps.

These calculations demonstrate how different quantities of data transfer rates can be understood and translated into more practical, real-world measurements.