Megabytes per hour to Gibibits per second conversion

How to convert megabytes per hour to gibibits per second?

To convert from Megabytes per hour (MB/hr) to Gibibits per second (Gib/s), it's essential to first understand the relationships between the various units involved and the two numbering systems: base 10 and base 2.

Base 10 (Decimal System)

1 Megabyte (MB) = 1,000,000 bytes 1 bit = 1/8 byte 1 Gigabit (Gb) = 1,000,000,000 bits

Base 2 (Binary System)

1 Mebibyte (MiB) = 2^20 bytes = 1,048,576 bytes 1 bit = 1/8 byte 1 Gibibit (Gib) = 2^30 bits = 1,073,741,824 bits

Conversion Process:

Base 10 Conversion

1. Convert Megabytes to Megabits: Since 1 byte = 8 bits, 1 MB = 8 megabits (Mb).

2. Convert MB/hr to Mb/hr: 1 MB/hr = 8 Mb/hr.

3. Convert Mb/hr to Mb/s: Since there are 3,600 seconds in an hour, (8 Mb/hr) / 3,600 = 8/3600 Mb/s = 0.002222 Mb/s.

4. Convert Mb/s to Gb/s: 0.002222 Mb/s / 1,000 = 0.000002222 Gb/s.

5. Convert Gb/s to Gib/s: 1 Gib = 2^30 bits, 1 GB (base 10) is 1,000,000,000 bits. Therefore, a much larger divisor compared to a Gib, leading to a much smaller number. For precision, it's easier to see that directly.

Using base 10, you end up far too precise. The approximation for easier understanding, if corrected:

Therefore: $0.002222Mb/s \times 1/1.073741824 \approx 0.00000207 \text{ in }\ Gib/s$ as it's smaller by ratio.

Base 2 Conversion:

1. Convert Megabytes (MB) to Mebibytes (MiB): 1 MB = 1,000,000 bytes, but, A MiB = 1,048,576 bytes.

2. Convert Mebibytes to bits using base 2 units: A Mebibyte contains $1 \, MiB = 1,048,576 \times 8 = 8,388,608$ bits. Thus 1 MiB/hr $= 8,388,608 / 3,600 \text{(seconds)} \approx 2,330.72 \, \text{bits/second}$.

3. Convert those bits to Gibibits: 2^30 bits per Gibibits $= 2,330.72 \text{ bits/second} \times (1 \text{ Gibibits } / 1,073,741,824 \text{ bits})$ Approximately $=2.16849^{-06}\ Gib/s$.

Therefore, using base 2, the data rate is approximately 0.000002169 Gib/s.

Real-World Examples for Other Quantities of Megabytes per Hour

1. Streaming Video:

   • An HD video stream, typically for standard quality, may have an approximate bitrate of 1.5 Megabytes per minute (which is 90 Megabytes per hour).
     • Using same calculations:
       • 720 MB/hour would be $0.02\ Gib/s$

2. Downloading Software Update:

   • Software updates may download at a rate of around 500 Megabytes per hour.
     • $500 MB/hr \rightarrow 11,1111 bits/sec \rightarrow 11*1000/3,600$:
       • Around 0.16 \ Gib/s

3. Web Browsing:

   • General web browsing can consume around 10 Megabytes per hour.
     • $taking step same : From base 2, $0.00000021 \ Gib/s

Conclusion:

For analytical accuracy, base 2 conversion is far practical giving 1 a very aproxqdance for unit where above direct does not need estimations. Real-world practical enough gives this.`