Kibibits per second to Megabytes per day conversion

How to convert kibibits per second to megabytes per day?

To convert from Kibibits per second (Kib/s) to Megabytes per day (MB/day), we need to account for the conversion between units of time, bits and bytes, and the different numerical bases (base 10 and base 2).

Base 2 (Binary System)

1 Kibibit (Kib) = 2^10 bits = 1024 bits. 1 Megabyte (MB, binary) = 2^20 bytes = 1,048,576 bytes. 1 byte = 8 bits.

Steps:

1. Convert Kibibits per second to bits per second: $1 \text{ Kib/s} = 1024 \text{ bits/second}$

2. Convert bits per second to bytes per second: $\frac{1024 \text{ bits}}{8} = 128 \text{ bytes/second}$

3. Convert bytes per second to bytes per day (seconds per day = 86400): $128 \text{ bytes/second} \times 86400 \text{ seconds/day} = 11,059,200 \text{ bytes/day}$

4. Convert bytes per day to Megabytes (using binary definition): $\frac{11,059,200 \text{ bytes/day}}{1,048,576 \text{ bytes/MB}} \approx 10.54 \text{ MB/day}$

Base 10 (Decimal System)

In the decimal (SI) system, 1 Megabyte (MB, decimal) = 1,000,000 bytes.

Steps:

1. Convert Kibibits per second to bits per second (no change from above): $1 \text{ Kib/s} = 1024 \text{ bits/second}$

2. Convert bits per second to bytes per second: $\frac{1024 \text{ bits}}{8} = 128 \text{ bytes/second}$

3. Convert bytes per second to bytes per day (seconds per day = 86400): $128 \text{ bytes/second} \times 86400 \text{ seconds/day} = 11,059,200 \text{ bytes/day}$

4. Convert bytes per day to Megabytes (using decimal definition): $\frac{11,059,200 \text{ bytes/day}}{1,000,000 \text{ bytes/MB}} = 11.0592 \text{ MB/day}$

Summary

• Under base 2 (binary), 1 Kibibits per second is approximately 10.54 Megabytes per day.
• Under base 10 (decimal), 1 Kibibits per second is 11.0592 Megabytes per day.

Real-World Examples

1. Streaming Services Data Rates: Video streaming services might have different data rates. For example, a lower quality streaming service might use 500 Kib/s:

   • Base 2: $500 \times 10.54 = 5270 \text{ MB/day} \approx 5.27 \text{ GB/day}$.
   • Base 10: $500 \times 11.0592 = 5529.6 \text{ MB/day} \approx 5.53 \text{ GB/day}$.

2. IoT Devices Data Usage: A small IoT sensor transmitting data at 10 Kib/s:

   • Base 2: $10 \times 10.54 = 105.4 \text{ MB/day} \approx 0.1054 \text{ GB/day}$.
   • Base 10: $10 \times 11.0592 = 110.592 \text{ MB/day} \approx 0.1106 \text{ GB/day}$.

3. Internet Speeds: A modest residential internet connection speed of 1000 Kib/s:

   • Base 2: $1000 \times 10.54 = 10,540 \text{ MB/day} \approx 10.54 \text{ GB/day}$.
   • Base 10: $1000 \times 11.0592 = 11,059.2 \text{ MB/day} \approx 11.06 \text{ GB/day}$.

These conversions help in understanding the data rates in different contexts and how they accumulate over longer periods.