bits per day to Tebibytes per second conversion

How to convert bits per day to tebibytes per second?

Sure, to convert from bits per day (bpd) to Tebibytes per second (TiB/s), we need to understand the relationship between these units of measure. First, let’s take a look at the conversions needed for both base 10 (decimal) and base 2 (binary) systems.

1. Conversion Factors:

   • There are $86,400$ seconds in a day (24 hours/day * 60 minutes/hour * 60 seconds/minute).
   • For base 2 (binary):
     • $1$ Tebibyte ($1 \ TiB$) $= 2^{40}$ bytes
     • $1$ byte $= 8$ bits $\Rightarrow 2^{40}$ bytes $= 8 \times 2^{40}$ bits $= 2^{43}$ bits.
   • For base 10 (decimal):
     • $1$ Terabyte ($1 \ TB$) $= 10^{12}$ bytes
     • $1$ byte $= 8$ bits $\Rightarrow 10^{12}$ bytes $= 8 \times 10^{12}$ bits $= 8 \times 10^{12}$ bits.

2. Conversion Process:

   • Bits per day to Tebibytes per second (base 2): $1 \ bpd$ $= \frac{1 \ \text{bit}}{86,400 \ \text{seconds}}$ $= \frac{1}{86,400} \ \text{bits per second}$

     To convert to Tebibytes per second: $\Bigg(\frac{1}{86,400}\Bigg) \text{bits per second} \times \Bigg(\frac{1 \ \text{TiB}}{2^{43} \ \text{bits}}\Bigg)$ $= \frac{1}{86,400 \times 2^{43}} \ \text{TiB/s} \approx 2.703292 \times 10^{-19} \ \text{TiB/s}$

   • Bits per day to Terabytes per second (base 10): $1 \ bpd$ $= \frac{1 \ \text{bit}}{86,400 \ \text{seconds}}$ $= \frac{1}{86,400} \ \text{bits per second}$

     To convert to Terabytes per second: $\Bigg(\frac{1}{86,400}\Bigg) \text{bits per second} \times \Bigg(\frac{1 \ \text{TB}}{8 \times 10^{12} \ \text{bits}}\Bigg)$ $= \frac{1}{86,400 \times 8 \times 10^{12}} \ \text{TB/s} \approx 1.446759 \times 10^{-22} \ \text{TB/s}$

3. Real-world Examples for Other Quantities of Bits per Day:

   • 1 Kilobit per day (1 Kbpd):

     • Base 2: $1 \ Kbpd = 1,000 \ bpd$
     • Base 10: $1 \ Kbpd = 1,024 \ bpd$

   • 1 Megabit per day (1 Mbpd):

     • Base 2: $1 \ Mbpd = 1,000,000 \ bpd$
     • Base 10: $1 \ Mbpd = 1,048,576 \ bpd$

   Example for practical use: If you have a home internet connection that downloads at 1 Megabit per day (which is quite slow):

    - Base 2: 
        $
        1 \ \text{Mbpd} = \frac{1,048,576}{2^{43} \times 86,400} \ \text{TiB/s} 
        \approx 2.703 \times 10^{-16} \ \text{TiB/s}
   

$ - Base 10: $1 \ \text{Mbpd} = \frac{1,000,000}{8 \times 10^{12} \times 86,400} \ \text{TB/s} \approx 1.447 \times 10^{-19} \ \text{TB/s}$

- **1 Gigabit per day (1 Gbpd):**
    - Base 2: $1 \ Gbpd = 1,000,000,000 \ bpd$ 
    - Base 10: $1 \ Gbpd = 1,073,741,824 \ bpd$

- **1 Terabit per day (1 Tbpd):**
    - Base 2: $1 \ Tbpd = 1,000,000,000,000 \ bpd$ 
    - Base 10: $1 \ Tbpd = 1,099,511,627,776 \ bpd$

Understanding these conversions can help in networking, data analysis, and many technical fields where data transfer rates are important.