bits per second to Tebibytes per day conversion

How to convert bits per second to tebibytes per day?

To convert bits per second (bps) to Tebibytes (TiB) per day, it is important to recognize that Tebibytes are based on binary (base 2) rather than decimal (base 10) measurements. Here is the step-by-step conversion process:

1. Bits per second to bits per day:

   • There are 86,400 seconds in a day.
   • $1 \text{ bit/second} \times 86,400 \text{ seconds/day} = 86,400 \text{ bits/day}$.

2. Binary (base 2) Conversion:

   • 1 Tebibyte (TiB) = $2^{40}$ bytes = $1,099,511,627,776$ bytes.
   • 1 byte = 8 bits.
   • Therefore, 1 Tebibyte = $1,099,511,627,776 \times 8$ bits = $8,796,093,022,208$ bits.

3. Conversion from bits per day to Tebibytes per day:

   • Tebibytes per day = $\frac{\text{bits per day}}{\text{bits per Tebibyte}}$.
   • Tebibytes per day = $\frac{86,400 \text{ bits/day}}{8,796,093,022,208 \text{ bits/TiB}}$.
   • Tebibytes per day = $\frac{86,400}{8,796,093,022,208} \approx 9.834 \times 10^{-6} \text{ TiB/day}$.

Thus, in binary (base 2), 1 bit per second is approximately $9.834 \times 10^{-6}$ Tebibytes per day.

For the decimal (base 10) conversion:

1. Bits per second to bits per day:

   • As previously, $1 \text{ bit/second} \times 86,400 \text{ seconds/day} = 86,400 \text{ bits/day}$.

2. Decimal (base 10) Conversion:

   • 1 Terabyte (TB) = $10^{12}$ bytes = $1,000,000,000,000$ bytes.
   • 1 byte = 8 bits.
   • Therefore, 1 Terabyte = $1,000,000,000,000 \times 8$ bits = $8,000,000,000,000$ bits.

3. Conversion from bits per day to Terabytes per day:

   • Terabytes per day = $\frac{\text{bits per day}}{\text{bits per Terabyte}}$.
   • Terabytes per day = $\frac{86,400 \text{ bits/day}}{8,000,000,000,000 \text{ bits/TB}}$.
   • Terabytes per day = $\frac{86,400}{8,000,000,000,000} \approx 1.08 \times 10^{-5} \text{ TB/day}$.

Thus, in decimal (base 10), 1 bit per second is approximately $1.08 \times 10^{-5}$ Terabytes per day.

Real-World Examples for Other Data Rates

1. 1 Megabit per second (Mbps):
   • 1 Mbps = $1,000,000$ bits per second.
   • Binary (Base 2):
     • $1,000,000 \text{ bps} \times 86,400 \text{ s/day} \approx 86.40 \times 10^9$ bits/day.
     • $\frac{86.40 \times 10^9}{8,796.093 \times 10^9} \approx 0.0098 \text{ TiB/day}$.

• Decimal (Base 10):
  • $1,000,000 \text{ bps} \times 86,400 \text{ s/day} = 86.40 \times 10^9$ bits/day.
  • $\frac{86.40 \times 10^9}{8 \times 10^12} = 0.0108 \text{ TB/day}$.

2. 100 Megabits per second (Mbps):
   • 100 Mbps = $100,000,000$ bits per second.
   • Binary (Base 2):
     • $100,000,000 \text{ bps} \times 86,400 \text{ s/day} \approx 8.64 \times 10^{12}$ bits/day.
     • $\frac{8.64 \times 10^{12}}{8,796.093 \times 10^9} \approx 0.981 \text{ TiB/day}$.

• Decimal (Base 10):
  • $100,000,000 \text{ bps} \times 86,400 \text{ s/day} = 8.64 \times 10^{12}$ bits/day.
  • $\frac{8.64 \times 10^{12}}{8 \times 10^{12}} = 1.08 \text{ TB/day}$.

3. 1 Gigabit per second (Gbps):
   • 1 Gbps = $1,000,000,000$ bits per second.
   • Binary (Base 2):
     • $1,000,000,000 \text{ bps} \times 86,400 \text{ s/day} \approx 86.4 \times 10^{12}$ bits/day.
     • $\frac{86.4 \times 10^{12}}{8,796.093 \times 10^9} \approx 9.834 \text{ TiB/day}$.

• Decimal (Base 10):
  • $1,000,000,000 \text{ bps} \times 86,400 \text{ s/day} = 86.4 \times 10^{12}$ bits/day.
  • $\frac{86.4 \times 10^{12}}{8 \times 10^{12}} = 10.8 \text{ TB/day}$.

These examples demonstrate how different data transfer rates convert to daily data volume in Tebibytes or Terabytes, depending on whether a binary or decimal base is used.