Gibibits per day to Gigabytes per second conversion

How to convert gibibits per day to gigabytes per second?

Sure, let's start by converting 1 Gibibit per day to Gigabytes per second.

First, we need to understand the differences between the units involved:

1 Gibibit (Gib) = $2^{30}$ bits (base 2, or binary) 1 Gigabyte (GB) = $10^9$ bytes (base 10, or decimal) 1 Gigabyte (GiB) = $2^{30}$ bytes (base 2, or binary)

1 byte = 8 bits

Conversion Steps:

1. Convert Gibibits to bits:

$1 \text{ Gib} = 2^{30} \text{ bits} = 1,073,741,824 \text{ bits}$

2. Convert bits to bytes:

$1,073,741,824 \text{ bits} \div 8 = 134,217,728 \text{ bytes}$

3. Convert bytes to Gigabytes (base 10):

$134,217,728 \text{ bytes} \div 10^9 = 0.134217728 \text{ GB}$

4. Convert days to seconds:

$1 \text{ day} = 24 \times 60 \times 60 = 86,400 \text{ seconds}$

5. Calculate data rate in Gigabytes per second (base 10):

$\frac{0.134217728 \text{ GB}}{86,400 \text{ seconds}} \approx 1.552 \times 10^{-6} \text{ GB/s}$

Conversion to Gigabytes (base 2):

1. Convert Gibibits to bytes directly (base 2):

$1 \text{ Gib} = 2^{30} \text{ bits}$ $1 \text{ Gib} = \frac{2^{30} \text{ bits}}{8} \text{ bytes} = 2^{27} \text{ bytes} = 134,217,728 \text{ bytes}$

2. Convert bytes to GiB:

$134,217,728 \text{ bytes} \div 2^{30} = 0.125 \text{ GiB}$

3. Calculate data rate in GiB per second (base 2), using seconds in a day calculated earlier:

$\frac{0.125 \text{ GiB}}{86,400 \text{ seconds}} \approx 1.447 \times 10^{-6} \text{ GiB/s}$

Real World Examples for Other Quantities of Gibibits per Day:

1. 10 Gibibits per day to Gigabytes per second (base 10):

$10 \text{ Gib/day} = 10 \times 1.552 \times 10^{-6} \text{ GB/s} = 1.552 \times 10^{-5} \text{ GB/s}$

2. 50 Gibibits per day to Gigabytes per second (base 10):

$50 \text{ Gib/day} = 50 \times 1.552 \times 10^{-6} \text{ GB/s} = 7.76 \times 10^{-5} \text{ GB/s}$

3. 100 Gibibits per day to Gigabytes per second (base 10):

$100 \text{ Gib/day} = 100 \times 1.552 \times 10^{-6} \text{ GB/s} = 1.552 \times 10^{-4} \text{ GB/s}$

Similarly, for Gigabytes per second (base 2):

1. 10 Gibibits per day to GiB per second:

$10 \text{ Gib/day} = 10 \times 1.447 \times 10^{-6} \text{ GiB/s} = 1.447 \times 10^{-5} \text{ GiB/s}$

2. 50 Gibibits per day to GiB per second:

$50 \text{ Gib/day} = 50 \times 1.447 \times 10^{-6} \text{ GiB/s} = 7.235 \times 10^{-5} \text{ GiB/s}$

3. 100 Gibibits per day to GiB per second:

$100 \text{ Gib/day} = 100 \times 1.447 \times 10^{-6} \text{ GiB/s} = 1.447 \times 10^{-4} \text{ GiB/s}$

I hope this helps clarify the conversions and provides some useful real-world examples!