Mebibytes per second to Gigabits per hour conversion

How to convert mebibytes per second to gigabits per hour?

Sure, let's go through the conversion step by step. The goal is to convert 1 Mebibyte per second (MiB/s) to Gigabits per hour (Gb/h).

Step 1: Understand the Units

1 MiB (Mebibyte) = $2^{20}$ bytes = 1,048,576 bytes 1 byte = 8 bits

1 hour = 3600 seconds

Step 2: Convert Mebibytes per second to Bytes per second

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

Step 3: Convert Bytes per second to Bits per second

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

Step 4: Convert Bits per second to Bits per hour

$8,388,608 \ \text{bits per second} \times 3600 \ \text{seconds per hour} = 30,199,948,800 \ \text{bits per hour}$

Step 5: Convert Bits per hour to Gigabits per hour

$30,199,948,800 \ \text{bits per hour} \div 1,000,000,000 \ \text{bits per Gigabit} = 30.1999488 \ \text{Gigabits per hour}$

Base 10 vs Base 2

For Base 2:

We've already done the Base 2 conversion: $1 \ \text{MiB/s (Base 2)} = 30.1999488 \ \text{Gb/h (Base 2)}$

For Base 10:

1 Megabyte (MB) = $10^6$ bytes = 1,000,000 bytes (for base 10 convention) 1 byte = 8 bits

1 Megabyte per second (MB/s) in base 10: $1 \ \text{MB/s} = 1,000,000 \ \text{bytes per second}$ $1,000,000 \ \text{bytes per second} \times 8 \ \text{bits per byte} = 8,000,000 \ \text{bits per second}$ $8,000,000 \ \text{bits per second} \times 3600 \ \text{seconds per hour} = 28,800,000,000 \ \text{bits per hour}$ $28.8 \ \text{Gigabits per hour (Base 10)}$

Summary

• Base 2 (Mebibytes): 1 MiB/s = 30.1999488 Gb/h
• Base 10 (Megabytes): 1 MB/s = 28.8 Gb/h

Real World Examples for Other Quantities of Mebibytes per Second

1. 10 MiB/s:

   • Base 2: $\approx 301.999488$ Gb/h
   • Base 10: $\approx 288$ Gb/h

2. 50 MiB/s:

   • Base 2: $\approx 1509.99744$ Gb/h
   • Base 10: $\approx 1440$ Gb/h

3. 100 MiB/s:

   • Base 2: $\approx 3019.99488$ Gb/h
   • Base 10: $\approx 2880$ Gb/h

These conversions are useful to understand when dealing with network equipment, data storage, and various IT infrastructures, where accurate data transfer rates are critical.