Gibibits per hour to Mebibytes per day conversion

How to convert gibibits per hour to mebibytes per day?

To convert Gibibits per hour to Mebibytes per day, we need to follow the steps of conversion carefully. We’ll first clarify the units involved:

1 Gibibit = $2^{30}$ bits (binary prefix) 1 Mebibyte = $2^{20}$ bytes (binary prefix) 1 byte = 8 bits

Given that:

1 Gibibit per hour (Gibibits/hr) needs to be converted to Mebibytes per day (Mebibytes/day).

Conversion steps:

1. Convert Gibibits to bits: $1 \text{ Gibibit} = 2^{30} \text{ bits}$

2. Convert bits to bytes (since there are 8 bits in a byte): $2^{30} \text{ bits} = \frac{2^{30}}{8} \text{ bytes} = 2^{27} \text{ bytes}$

3. Convert bytes to Mebibytes (since there are $2^{20}$ bytes in a Mebibyte): $2^{27} \text{ bytes} = \frac{2^{27}}{2^{20}} \text{ Mebibytes} = 2^7 \text{ Mebibytes} = 128 \text{ Mebibytes}$

So, $1 \text{ Gibibit/hr} = 128 \text{ Mebibytes/hr}$.

Now, we need to convert this rate from per hour to per day:

4. There are 24 hours in a day: $128 \text{ Mebibytes/hr} \times 24 \text{ hr/day} = 3072 \text{ Mebibytes/day}$

Answer for base 2 (binary):

1 Gibibit per hour = 3072 Mebibytes per day.

Real-world examples for other quantities of Gibibits per hour:

Example 1: 2 Gibibits per hour

$2 \text{ Gibibits/hr} \times 128 \text{ Mebibytes/hr per Gibibit} = 256 \text{ Mebibytes/hr}$ $256 \text{ Mebibytes/hr} \times 24 \text{ hr/day} = 6144 \text{ Mebibytes/day}$

Example 2: 5 Gibibits per hour

$5 \text{ Gibibits/hr} \times 128 \text{ Mebibytes/hr per Gibibit} = 640 \text{ Mebibytes/hr}$ $640 \text{ Mebibytes/hr} \times 24 \text{ hr/day} = 15360 \text{ Mebibytes/day}$

If the quantities were to be interpreted using base 10 (decimal), you would generally use gigabits and megabytes instead of gibibits and mebibytes. However, for clarity, the binary (base 2) units are more precise because they match the conversions described above.

In base 10:

1 Gibibit (binary) ≈ 1.07374 Gigabits (decimal) 1 Mebibyte (binary) ≈ 1.04858 Megabytes (decimal)

Thus, 1 Gibibit per hour ≈ 128 × 1.04858 Megabytes per hour = 134.22 Megabytes per hour (approximately).

$134.22 \text{ Megabytes/hr} \times 24 \text{ hr/day} ≈ 3221.28 \text{ Megabytes/day}$

Answer for base 10 (approximate):

1 Gibibit per hour (binary) ≈ 3221.28 Megabytes per day (decimal).

Remember, these calculations provide an approximate conversion due to the switch from binary to decimal units in the base 10 example.