Mebibytes per hour to Gigabits per second conversion

How to convert mebibytes per hour to gigabits per second?

Certainly! To convert MeB (Mebibytes) per hour to Gb (Gigabits) per second, we'll need to follow these steps:

1. Convert Mebibytes to Mebibits.
2. Convert Mebibits to Gigabits.
3. Convert hours to seconds.

Step-by-Step Conversion

1. Mebibytes to Mebibits

There are 8 bits in a byte, so:

$1 \text{ Mebibyte (MiB)} = 1 \times 2^{20} \text{ bytes} = 2^{20} \times 8 \text{ bits} = 2^{20} \times 8 \text{ bits} = 8 \times 2^{20} \text{ bits} = 8 \times 1,048,576 \text{ bits} = 8,388,608 \text{ bits} = 2^{23} \text{ bits}$

So, one Mebibyte is equivalent to 8 Mebibits:

$1 \text{ MiB} = 8 \text{ Mebibits (Mib)}$

2. Mebibits to Gigabits

There are 1024 Mebibits in a Gibibit (GiB), and one Gibibit is equivalent to one Gigabit (Gbit), assuming base 2:

$1 \text{ GiB} = 1024 \text{ Mib}$

Therefore,

$1 \text{ Mib} = \frac{1}{1024} \text{ GiB}$

And,

$1 \text{ GiB} = 1 \text{ Gbit}$

So,

$1 \text{ Mib} = \frac{1}{1024} \text{ Gbit}$

And hence,

$8 \text{ Mib (from 1 MiB)} = 8 \times \frac{1}{1024} \text{ Gbit} = \frac{8}{1024} \text{ Gbit} = \frac{1}{128} \text{ Gbit} \approx 0.0078125 \text{ Gbit}$

3. Hours to Seconds

There are 3600 seconds in an hour:

$\text{1 hour} = 3600 \text{ seconds}$

So, the rate in Gigabits per second (Gbit/s) is:

$\text{(0.0078125 Gbit)} \div 3600 \text{ seconds} \approx 2.1701389 \times 10^{-6} \text{ Gbit/s}$

Alternative: Base 10 Conversion

If we use base 10: 1 Mebibyte (MiB) is approximately 1.048576 Megabytes (MB). In base 10:

$1 \text{ MB} = 1 \times 10^6 \text{ bytes} = 8 \times 10^6 \text{ bits}$

So one Mebibyte is equivalent to:

$1 \text{ MiB} \approx 8.388608 \times 10^6 \text{ bits (as before)}$

1 Mebibyte per hour:

$1 \text{ MiB/hour} \approx \frac{8.388608 \times 10^6 \text{ bits}}{3600 \text{ seconds}} \approx 2330.169 \text{ bits/second}$

Convert bits/second to Gigabits/second (Gbps):

$2330.169 \text{ bits/second} \approx 2.330169 \times 10^{-3} \text{ Gbps} = 0.002330169 \text{ Gbps}$

Real-World Examples of Data Transfer in Mebibytes per Hour

• Internet Data Cap:

  • For a certain ISP data cap: 5 GB per day = 5,120 MiB/day = 213.33 MiB/hour ≈ $\approx 5.94241 \times 10^{-4} \text{ Gbps}$.

• Streaming Video:

  • A typical HD streaming service might use approximately 3 MiB per minute: $3 \text{ MiB/minute} = 180 \text{ MiB/hour} ≈ 4.88281 \times 10^{-4} \text{ Gbps}$.

• Data Backup/Sync:

  • A cloud storage service that syncs 200 MiB of data per hour ≈ 5.86 MiBps = $\approx 1.587301 \times 10^{-4} \text{ Gbps}$.

These steps and examples assume base 2 calculations were closest for determining realistic communication rates.