Kibibits per day to Megabytes per second conversion

How to convert kibibits per day to megabytes per second?

To convert $1 \text{ Kibibit per day (Kibit/day)}$ to Megabytes per second (MBps), we need to understand the relationships between the units involved and then perform the appropriate conversions.

Understanding the Units

1. Data Size Units:

   • 1 Kibibit (Kibit) = $2^{10}$ bits = 1024 bits (base 2)
   • 1 Megabyte (MB) can either be $10^6$ bytes (base 10) or $2^{20}$ bytes (1048576 bytes, base 2).
   • 1 byte = 8 bits.

2. Time Units:

   • 1 day = 24 hours.
   • 1 hour = 3600 seconds.
   • Therefore, 1 day = $24 \times 3600 = 86400 \text{ seconds}$.

Conversion Process

Base 2 (Binary System)

1. Calculate Kibibits per second:

   • $1 \text{ Kibibit per day} = \frac{1024 \text{ bits}}{86400 \text{ seconds}}$.

2. Calculate Kibibits to Kilobytes:

   • Since 1 byte = 8 bits, we have $1 \text{ Kilobyte (KiB)} = 1024 \text{ bytes}$.
   • Therefore, $1 \text{ Kibibit} = \frac{1024 \text{ bits}}{8 \times 1024 \text{ bytes}} = \frac{1}{8}$ Kibibytes (KiB).

3. Convert to Megabytes (base 2):

   • 1 Kibibyte (KiB) = $2^{10}$ bytes = 1024 bytes.
   • 1 Megabyte (MB) = $2^{20}$ bytes.
   • So, $\frac{1}{8 \times 1024} \text{ Kibibytes} = \frac{1}{8 \times 1024 \times 1048576} \text{ MB}$.

4. Simplify the conversion:

   • From step 1, we have $\text{Kibibit per second} = \frac{1024}{86400}$.
   • Now, \text{ bytes per second} = \frac{1024 \text{ bits}}{8 \times 86400} = \frac{1024}{8 \times 86400} \text{ bytes}.

   Convert bytes per second to Megabytes per second:

   • $\frac{1024}{8 \times 86400} \div 1048576$.

5. Final conversion:

   • $\frac{1024 \text{ bits}}{8}= 128/86400 \text{ bytes} \approx 1.4763 \times 10^{-3} \text{ bytes per second}$.
   • Now convert to MB: $\approx \frac{1.4763 \times 10^{-3}}{1048576} \approx 1.408 \times 10^{-9} \text{ Megabytes per second}$.

Base 10 (Decimal System)

1. Bits to bytes:

   • $1 \text{ Kibibit} = 1024 \text{ bits}$.
   • Without conversion to KiB and direct conversion to MB (base 10, 1MB = $10^6$ bytes).
   • $\frac{1024 \text{ bits}}{8} = 128 \text{ bytes}$.

2. Convert per second:

   • $\frac{128}{86400} \approx 0.00148148 \text{ bytes per second}$.

3. Convert bytes to MB:

   • $\frac{0.00148148}{1000000} \approx 1.48148 \times 10^{-9} \text{ Megabytes per second}$.

Real World Examples

Low Transfer Rates:

• 1 Kibibit per day (Kibit/day): As calculated, it's very slow, approximately $1.408 \times 10^{-9}$ MBps.
• 100 Kibibits per day: Approximately $1.408 \times 10^{-7}$ MBps.
• 10000 Kibibits per day: Approximately $1.408 \times 10^{-5}$ MBps.

Significant Real World Quantities:

• 1 Mbps Internet Connection:Comparatively much faster, $1 \text{ Mbps} = 125 \text{ KBps}$, significantly faster than 1 Kibit/day.
• Streaming Video: Typically requires around 3-5 Mbps for HD quality, significantly higher than day-long transmissio rates.

These examples show that data rates equivalent to a few Kibibits per day are exceptionally slow compared to most modern data transfer requirements.