Bytes per day to Gibibits per second conversion

How to convert bytes per day to gibibits per second?

To convert data transfer rates from Bytes per Day (B/day) to Gibibits per Second (Gibps or Gb/s), you need to perform a two-step conversion: first to bytes per second (B/s), and then to Gibibits per second. Whether the answer depends on base 10 (i.e., Gigabits) or base 2 (i.e., Gibibits) is important, as computers use base 2 for binary representation.

Step-by-step conversion:

1. Convert Bytes per Day to Bytes per Second (B/s):

1 Byte/day = $\frac{1 \text{ Byte}}{24 \text{ hours} \times 60 \text{ minutes/hour} \times 60 \text{ seconds/minute}}$

$= \frac{1 \text{ Byte}}{86,400 \text{ seconds}}$

$\approx 1.1574 \times 10^{-5} \text{ Bytes per second}$

2. Convert Bytes per Second (B/s) to Gibibits per Second (Gibps or Gb/s):

For base 2:

• 1 Gibibit (Gib) = $2^{30}$ bits = 1,073,741,824 bits.
• 1 Byte = 8 bits.

So,

$1 \text{ Byte per day} = 1.1574 \times 10^{-5} \text{ B/s} \times 8 \text{ bits/Byte}$ $= 9.2593 \times 10^{-5} \text{ bits/second}$

$1 \text{ Gibibit per second} = 1,073,741,824 \text{ bits}$

Therefore,

$9.2593 \times 10^{-5} \text{ bits/second} \times \frac{1 \text{ Gibibit}}{1,073,741,824 \text{ bits}}$ $= 8.625 \times 10^{-14} \text{ Gibibits per second}$

So, 1 Byte/day ≈ 8.625 × 10⁻¹⁴ Gibibits per Second in base 2.

For base 10:

• 1 Gigabit (Gb) = $10^9$ bits.
• 1 Byte = 8 bits.

So,

$1 \text{ Byte per day} = 1.1574 \times 10^{-5} \text{ B/s} \times 8 \text{ bits/Byte}$ $= 9.2593 \times 10^{-5} \text{ bits/second}$

$1 \text{ Gigabit per second} = 1,000,000,000 \text{ bits}$

Therefore,

$9.2593 \times 10^{-5} \text{ bits/second} \times \frac{1 \text{ Gigabit}}{1,000,000,000 \text{ bits}}$ $= 9.259 \times 10^{-14} \text{ Gigabits per second}$

So, 1 Byte/day ≈ 9.259 × 10⁻¹⁴ Gigabits per Second in base 10.

Real-world examples for other quantities of Bytes per day:

1. 1 Kilobyte (KB) per day:

   • $1 KB/day = 1024 \text{ Bytes/day} = 1024 \times 8.625 \times 10^{-14} \text{ Gibps}$
   • $≈ 8.84 \times 10^{-11} \text{ Gibps}$

2. 1 Megabyte (MB) per day:

   • $1 MB/day = 1024 \times 1024 \text{ Bytes/day} = 1,048,576 \text{ Bytes/day}$
   • $= 1,048,576 \times 8.625 \times 10^{-14} \text{ Gibps}$
   • $≈ 9.04 \times 10^{-8} \text{ Gibps}$

3. 1 Gigabyte (GB) per day:

   • $1 GB/day = 1024^3 \text{ Bytes/day} = 1,073,741,824 \text{ Bytes/day}$
   • $= 1,073,741,824 \times 8.625 \times 10^{-14} \text{ Gibps}$
   • $≈ 9.25 \times 10^{-5} \text{ Gibps}$

4. Typical Usage Example:

   • Video Streaming Data Use: If you consume 1 GB per day streaming content, that translates to approximately 9.25 × 10⁻⁵ Gibibits per second or about 0.0001 Gb/s in base 2. This would be a very low data rate compared to average internet speeds and data consumption.

By breaking these conversions step by step and understanding both base 2 and base 10 representations, you can appreciate the small transfers we consider in Bytes/day in the context of network speeds typically measured in higher orders of magnitude, like Gibibits or Gigabits per second.