Mebibits per hour to Tebibytes per second conversion

How to convert mebibits per hour to tebibytes per second?

Certainly! Let's break down the conversion step by step, explaining both base 10 (common usage) and base 2 (binary, which is typically used in computing).

1. Understanding the Units

1. Mebibit (Mib): In base 2, a Mebibit is $2^{20}$ bits, which equals $1,048,576$ bits.
2. Tebibyte (TiB): In base 2, a Tebibyte is $2^{40}$ bytes, which equals $1,099,511,627,776$ bytes. Since 1 byte = 8 bits, a Tebibyte in bits is $8 \times 1,099,511,627,776 = 8,796,093,022,208$ bits.

2. Converting Mebibits per Hour to Tebibytes per Second

First, convert Mebibits per hour (Mib/h) to bits per second (bps), then convert bits per second to Tebibytes per second (TiB/s).

Base 2 (Binary)

1. Convert Mebibits per hour to bits per hour:

   • $1 \text{ Mib} = 1,048,576 \text{ bits}$
   • So, $1 \text{ Mib/h} = 1,048,576 \text{ bits per hour}$

2. Convert bits per hour to bits per second:

   • There are $3600$ seconds in an hour.
   • $\text{Bits per second} = \frac{1,048,576 \text{ bits}}{3600 \text{ seconds}}$
   • $\text{Bits per second} \approx 291.27 \text{ bps}$

3. Convert bits per second to Tebibytes per second:

   • 1 Tebibyte (TiB) = 8,796,093,022,208 bits.
   • $\text{TiB/s} = \frac{291.27 \text{ bps}}{8,796,093,022,208 \text{ bps/TiB}}$
   • $\text{TiB/s} \approx 3.31 \times 10^{-11} \text{ TiB/s}$

Base 10 (Decimal)

In decimal, the conversion is based on the following:

1. Mebibit (Mbits) in decimal: $1 \text{ Mb} = 10^6 \text{ bits}$

2. Tebibyte (TByte) in decimal: $1 \text{ TB} = 10^{12} \text{ bytes}$, and since 1 byte = 8 bits, $1 \text{ TB} = 8 \times 10^{12} \text{ bits} = 8,000,000,000,000 \text{ bits}$.

3. Convert Mebibits per hour to bits per hour:

   • $1 \text{ Mibit} = 1,000,000 \text{ bits}$ in decimal.
   • $1 \text{ Mib/h} = 1,000,000 \text{ bits per hour}$

4. Convert bits per hour to bits per second:

   • $\text{Bits per second} = \frac{1,000,000 \text{ bits}}{3600 \text{ seconds}}$
   • $\text{Bits per second} \approx 277.78 \text{ bps}$

5. Convert bits per second to Tebibytes per second:

   • 1 Tebibyte (TiB) = 8,000,000,000,000 bits.
   • $\text{TByte/s} = \frac{277.78 \text{ bps}}{8,000,000,000,000 \text{ bps/TByte}}$
   • $\text{TByte/s} \approx 3.47 \times 10^{-11} \text{ TByte/s}$

Real World Examples

1. Download Speeds:

• 10 Mebibits per hour:
  • Base 2: $10 \times 3.31 \times 10^{-11}$ TiB/s $= 3.31 \times 10^{-10}$ TiB/s
  • Base 10: $10 \times 3.47 \times 10^{-11}$ TByte/s $= 3.47 \times 10^{-10}$ TByte/s

2. Streaming Services:

• 100 Mebibits per hour:
  • Base 2: $100 \times 3.31 \times 10^{-11}$ TiB/s $= 3.31 \times 10^{-9}$ TiB/s
  • Base 10: $100 \times 3.47 \times 10^{-11}$ TByte/s $= 3.47 \times 10^{-9}$ TByte/s

3. Data Backups:

• 500 Mebibits per hour:
  • Base 2: $500 \times 3.31 \times 10^{-11}$ TiB/s $= 1.655 \times 10^{-8}$ TiB/s
  • Base 10: $500 \times 3.47 \times 10^{-11}$ TByte/s $= 1.735 \times 10^{-8}$ TByte/s

Conclusion

The conversions between Mebibits per hour to Tebibytes per second illustrate the granularity and the relatively tiny values when shifting from an hourly to a second-based rate and a smaller to a larger unit. Note that the values differ slightly depending on whether you are using base 2 (binary) or base 10 (decimal). The difference, however, is relatively small.