Gibibits per second to Kibibytes per day conversion

How to convert gibibits per second to kibibytes per day?

Converting 1 Gibibit per second (Gibit/s) to Kibibytes per day involves several steps, including converting between different units of data and then scaling to the appropriate time frame. Let’s break down the conversion for both base-2 (binary) and base-10 (decimal) systems.

Base-2 (Binary) Conversion

1 Gibibit (Gibit) is equal to $2^{30}$ bits:

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

1 Kibibyte (KiB) is equal to $2^{10}$ bytes, and since 1 byte is 8 bits:

$1 \text{ KiB} = 2^{10} \text{ bytes} = 1,024 \text{ bytes}$

Thus, 1 Kibibyte in bits (since 1 byte = 8 bits):

$1 \text{ KiB} = 1,024 \text{ bytes} \times 8 \text{ bits/byte} = 8,192 \text{ bits}$

Now, converting 1 Gibibit per second to Kibibytes per second:

$1 \text{ Gibit/second} = 1,073,741,824 \text{ bits/second}$

To find this in Kibibytes per second (KiB/s):

$\text{KiB/s} = \frac{1,073,741,824 \text{ bits/second}}{8,192 \text{ bits/KiB}} = 131,072 \text{ KiB/s}$

Next, we convert KiB/s to KiB/day (seconds to days):

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

Multiplying by the number of seconds in a day:

$\text{KiB/day} = 131,072 \text{ KiB/s} \times 86,400 \text{ s/day} = 11,310,628,864 \text{ KiB/day}$

Base-10 (Decimal) Conversion

1 Gibibit (Gibit) is defined as $10^9$ bits in base-10:

$1 \text{ Gibit} (Base-10) = 10^9 \text{ bits}$

1 Kilobyte (KB) is $10^3$ bytes, and 1 byte is 8 bits:

$1 \text{ KB} = 1,000 \text{ bytes}$

Thus, 1 Kilobyte in bits:

$1 \text{ KB} = 1,000 \text{ bytes} \times 8 \text{ bits/byte} = 8,000 \text{ bits}$

Now, converting 1 Gibibit per second to Kilobytes per second:

$1 \text{ Gibit/second (Base-10)} = 1,000,000,000 \text{ bits/second}$

To find this in Kilobytes per second (KB/s):

$\text{KB/s} = \frac{1,000,000,000 \text{ bits/second}}{8,000 \text{ bits/KB}} = 125,000 \text{ KB/s}$

Next, we convert KB/s to KB/day:

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

Multiplying by the number of seconds in a day:

$\text{KB/day} = 125,000 \text{ KB/s} \times 86,400 \text{ s/day} = 10,800,000,000 \text{ KB/day}$

Real World Examples

1. 100 Gibibits per second:

   • Binary system (Base-2): $100 \times 11,310,628,864 \text{ KiB/day} = 1,131,062,886,400 \text{ KiB/day}$
   • Decimal system (Base-10): $100 \times 10,800,000,000 \text{ KB/day} = 1,080,000,000,000 \text{ KB/day}$

2. 10 Gibibits per second:

   • Binary system (Base-2): $10 \times 11,310,628,864 \text{ KiB/day} = 113,106,288,640 \text{ KiB/day}$
   • Decimal system (Base-10): $10 \times 10,800,000,000 \text{ KB/day} = 108,000,000,000 \text{ KB/day}$

3. 1.5 Gibibits per second:

   • Binary system (Base-2): $1.5 \times 11,310,628,864 \text{ KiB/day} = 16,965,943,296 \text{ KiB/day}$
   • Decimal system (Base-10): $1.5 \times 10,800,000,000 \text{ KB/day} = 16,200,000,000 \text{ KB/day}$

These examples demonstrate the magnitude of data transfer at high rates over a 24-hour period, showing significant differences between Base-2 and Base-10 calculations.