Terabytes per day to Gibibits per second conversion

How to convert terabytes per day to gibibits per second?

Sure, let's break down the conversion of 1 Terabyte per day (TB/day) to Gibibits per second (Gib/s), taking into account both base 10 (decimal) and base 2 (binary) systems.

Base 10 Conversion

1 Terabyte (TB) in base 10 is defined as $1 \times 10^{12}$ bytes.

1 byte = 8 bits

1 day = 86400 seconds (24 hours * 60 minutes * 60 seconds)

To convert TB/day to bits/second: $\text{(1 TB/day) to bits/s} = \frac{1 \times 10^{12} \text{ bytes}}{86400 \text{ seconds}} \times 8 \text{ bits/byte}$

$= \frac{1 \times 10^{12} \times 8}{86400}$

$= \frac{8 \times 10^{12}}{86400}$

$= 9.259 \times 10^{7} \text{ bits/second}$

Now, to convert bits/second to Gibibits/second (Gib/s):

1 Gibibit (Gib) = $2^{30}$ bits (base 2 definition)

$\text{Gib/s} = \frac{9.259 \times 10^{7}}{2^{30}}$

$\approx \frac{9.259 \times 10^{7}}{1.073 \times 10^{9}}$

$\approx 0.0862 \text{ Gibibits/second (Gib/s)}$

Base 2 Conversion

In base 2, 1 Terabyte (TB) is defined as $2^{40}$ bytes.

Again, converting TB/day to bits/second in base 2: $\text{(1 TB/day) to bits/s} = \frac{2^{40} \text{ bytes}}{86400 \text{ seconds}} \times 8 \text{ bits/byte}$

$= \frac{2^{40} \times 8}{86400}$

$= \frac{8 \times 2^{40}}{86400}$

Since $2^{40} = 1.0995 \times 10^{12}$, the formula simplifies to: $= \frac{8 \times 1.0995 \times 10^{12}}{86400}$

$= \frac{8.796 \times 10^{12}}{86400}$

$= 1.017 \times 10^{8} \text{ bits/second}$

Now convert bits/second to Gibibits/second (Gib/s): $\text{Gib/s} = \frac{1.017 \times 10^{8}}{2^{30}}$

$= \frac{1.017 \times 10^{8}}{1.073 \times 10^{9}}$

$\approx 0.0948 \text{ Gibibits/second (Gib/s)}$

Summary

• Base 10: 1 TB/day is approximately 0.0862 Gib/s.
• Base 2: 1 TB/day is approximately 0.0948 Gib/s.

Real World Examples

• 10 TB/day:

  • Base 10: $10 \times 0.0862 = 0.862$ Gib/s
  • Base 2: $10 \times 0.0948 = 0.948$ Gib/s

• 100 TB/day:

  • Base 10: $100 \times 0.0862 = 8.62$ Gib/s
  • Base 2: $100 \times 0.0948 = 9.48$ Gib/s

• 1 PB/day (Petabyte):

  • Base 10: $1,000 \times 0.0862 = 86.2$ Gib/s
  • Base 2: $1,000 \times 0.0948 = 94.8$ Gib/s

These examples provide a sense of the data transfer rates for varying amounts of data traffic per day in terms of Gibibits per second.