Mebibytes per second to Megabits per day conversion

How to convert mebibytes per second to megabits per day?

Sure, let's dive into the conversion between Mebibytes per second and Megabits per day, and examine the difference between using base 10 and base 2 systems. First, we need to understand the units involved:

1. Mebibyte (MiB):

   • Base 2: 1 Mebibyte (MiB) = 2^20 bytes = 1,048,576 bytes

2. Megabit (Mb):

   • Base 10: 1 Megabit (Mb) = 10^6 bits = 1,000,000 bits

3. Seconds to Days:

   • 1 day = 24 hours = 24 * 60 minutes = 24 * 60 * 60 seconds = 86,400 seconds

Base 2 Conversion (Binary)

1. Step 1: Convert Mebibytes (MiB) to bytes per second:

   • $1 \text{ MiB/second} = 1,048,576 \text{ bytes/second}$

2. Step 2: Convert bytes to bits:

   • $1 \text{ byte} = 8 \text{ bits}$
   • $1,048,576 \text{ bytes/second} \times 8 \text{ bits/byte} = 8,388,608 \text{ bits/second}$

3. Step 3: Calculate the total bits in a day:

   • $8,388,608 \text{ bits/second} \times 86,400 \text{ seconds} = 724,775,731,200 \text{ bits/day}$

4. Step 4: Convert bits to Megabits:

   • $1 \text{ Megabit} = 1,000,000 \text{ bits}$
   • $724,775,731,200 \text{ bits} \div 1,000,000 = 724,775.7312 \text{ Megabits/day}$

Base 10 Conversion (Decimal)

1. Step 1: Convert Mebibytes to bytes per second (base 10 uses Megabytes rather than Mebibytes):

   • $1 \text{ MiB} = 1,048,576 \text{ bytes} \approx 1.048576 \text{ Megabytes (MB)}$
   • Assume for simplification 1 MiB ≈ 1.048576 MB

2. Step 2: Convert Megabytes to Megabits directly:

   • $1 \text{ MB} = 8 \text{ Megabits (Mb)}$
   • $1.048576 \text{ MB/second} \times 8 = 8.388608 \text{ Megabits/second}$

3. Step 3: Calculate the total Megabits in a day:

   • $8.388608 \text{ Mb/second} \times 86,400 \text{ seconds} = 724,775.4528 \text{ Megabits/day}$

Summary

• Base 2: $724,775.7312 \text{ Megabits/day}$
• Base 10: $724,775.4528 \text{ Megabits/day}$

The difference is minor but nonetheless present due to the nature of using binary (base 2) versus decimal (base 10) systems.

Real World Examples

• A fiber optic internet connection might deliver speeds around 1 GiB (Gibibyte) per second. This translates to $1 \text{ GiB} = 1,024 \text{ MiB}$ which is very high-speed internet access.
• USB 3.0 ports deliver data transfer speeds of up to 5 Gbps (Gigabits per second). This is roughly equivalent to a theoretical maximum of 625 MB/s (Megabytes per second) or about 596.046 MiB/s.
• HD video streaming typically requires speeds of 5 Mbps (Megabits per second) for a 1080p resolution stream, which translates to a data rate of around 0.625 MiB/s.

These examples highlight how various data transmission rates are utilized in everyday technology, providing context for Mebibytes per second as a unit of measure.