Megabits per second to Kibibytes per day conversion

How to convert megabits per second to kibibytes per day?

Certainly! Let's break down the conversion of 1 Megabit per second (Mbps) to Kibibytes per day (KiB/day) and see how it differs when you use base 10 (decimal) versus base 2 (binary) systems.

Base 10 (Decimal System)

In the decimal system:

• 1 Megabit (Mb) is equal to 1,000,000 bits.
• 1 byte = 8 bits.

1. Convert Megabits to Megabytes: $1 \, \text{Mbps} = \frac{1,000,000 \, \text{bits/second}}{8} = 125,000 \, \text{bytes/second}$

2. Convert Megabytes to Kilobytes (base 10): $125,000 \, \text{bytes/second} = \frac{125,000}{1,000} = 125 \, \text{Kilobytes/second (KB/s)}$

3. Convert Kilobytes per second to Kilobytes per day: $125 \, \text{KB/s} \times 60 \, \text{seconds/min} \times 60 \, \text{min/hour} \times 24 \, \text{hours/day} = 10,800,000 \, \text{Kilobytes/day}$

4. Convert Kilobytes to Kibibytes (base 2): In base 10: $10,800,000 \, \text{KB/day}$

   In base 2: Since 1 KB = 1,024 bytes in base 2: $\frac{10,800,000 \, \text{KB}}{1.024} \approx 10,546,875 \, \text{KiB/day}$

Base 2 (Binary System)

In the binary system:

• 1 Megabit (Mb) is still equal to 1,000,000 bits (since it's a measure by ISP standards).
• 1 byte = 8 bits.
• 1 Kibibyte (KiB) = 1,024 bytes.

1. Convert Megabits to Megabytes: $1 \, \text{Mbps} = \frac{1,000,000 \, \text{bits/second}}{8} = 125,000 \, \text{bytes/second}$

2. Convert bytes to Kibibytes: $125,000 \, \text{bytes/second} = \frac{125,000}{1,024} \approx 122.07 \, \text{KiB/second}$

3. Convert Kibibytes per second to Kibibytes per day: $122.07 \, \text{KiB/second} \times 60 \, \text{seconds/min} \times 60 \, \text{minutes/hour} \times 24 \, \text{hours/day} \approx 10,538,688 \, \text{KiB/day}$

Summary:

• In base 10 conversion, $\approx 10,800,000 \, \text{Kilobytes/day}$.
• In base 2 conversion, $\approx 10,538,688 \, \text{Kibibytes/day}$.

Real-World Examples at Different Data Rates

1. 10 Mbps:

   • Base 10: $10 \times 10,800,000 = 108,000,000 \, \text{KB/day}$
   • Base 2: $10 \times 10,538,688 = 105,386,880 \, \text{KiB/day}$

2. 50 Mbps:

   • Base 10: $50 \times 10,800,000 = 540,000,000 \, \text{KB/day}$
   • Base 2: $50 \times 10,538,688 = 526,934,400 \, \text{KiB/day}$

3. 100 Mbps:

   • Base 10: $100 \times 10,800,000 = 1,080,000,000 \, \text{KB/day}$
   • Base 2: $100 \times 10,538,688 = 1,053,868,800 \, \text{KiB/day}$

These conversions help you understand how much data is being transferred over a day at various data rates in different bases, which can be useful for network planning and data usage analysis.