Mebibits per second to Gigabytes per day conversion

How to convert mebibits per second to gigabytes per day?

Absolutely, let's work through the conversion step-by-step.

First, it's important to understand the relationship between these units:

1. Base 2 (Binary) Conversion:

   • 1 mebibit (Mib) = $2^{20}$ bits = 1,048,576 bits
   • 1 gibibyte (GiB) = $2^{30}$ bytes = 1,073,741,824 bytes
   • 1 byte = 8 bits

2. Base 10 (Decimal) Conversion:

   • 1 megabit (Mb) = $10^6$ bits = 1,000,000 bits
   • 1 gigabyte (GB) = $10^9$ bytes = 1,000,000,000 bytes
   • 1 byte = 8 bits

Base 2 (Binary) Conversion:

Step 1: Convert Mebibits per second to bits per second

1 Mib/s = 1,048,576 bits per second

Step 2: Convert bits per second to bytes per second

$\text{Bytes per second} = \frac{\text{Bits per second}}{8}$ $\text{Bytes per second} = \frac{1,048,576}{8} = 131,072 \text{ bytes/second}$

Step 3: Convert bytes per second to bytes per day

$\text{Bytes per day} = 131,072 \times 60 \times 60 \times 24$ $\text{Bytes per day} = 11,323,084,800 \text{ bytes/day}$

Step 4: Convert bytes per day to gibibytes per day

$\text{GiB per day} = \frac{\text{Bytes per day}}{1,073,741,824}$ $\text{GiB per day} = \frac{11,323,084,800}{1,073,741,824} \approx 10.55 \text{ GiB/day}$

Base 10 (Decimal) Conversion:

Step 1: Convert Mebibits per second to bits per second

1 Mib/s = 1,048,576 bits per second

Step 2: Convert bits per second to bytes per second

$\text{Bytes per second} = \frac{\text{Bits per second}}{8}$ $\text{Bytes per second} = \frac{1,048,576}{8} = 131,072 \text{ bytes/second}$

Step 3: Convert bytes per second to bytes per day

$\text{Bytes per day} = 131,072 \times 60 \times 60 \times 24$ $\text{Bytes per day} = 11,323,084,800 \text{ bytes/day}$

Step 4: Convert bytes per day to gigabytes per day

$\text{GB per day} = \frac{\text{Bytes per day}}{1,000,000,000}$ $\text{GB per day} = \frac{11,323,084,800}{1,000,000,000} \approx 11.32 \text{ GB/day}$

Summary:

• 1 Mib/s = 10.55 GiB/day using the base 2 (binary) conversion.
• 1 Mib/s = 11.32 GB/day using the base 10 (decimal) conversion.

Real-world Examples for Other Quantities:

• 5 Mib/s:

  • Base 2: $5 \times 10.55 = 52.75 \text{ GiB/day}$
  • Base 10: $5 \times 11.32 = 56.6 \text{ GB/day}$

• 10 Mib/s:

  • Base 2: $10 \times 10.55 = 105.5 \text{ GiB/day}$
  • Base 10: $10 \times 11.32 = 113.2 \text{ GB/day}$

• 50 Mib/s:

  • Base 2: $50 \times 10.55 = 527.5 \text{ GiB/day}$
  • Base 10: $50 \times 11.32 = 566 \text{ GB/day}$

These conversions illustrate how data rates typically used in network terms (like Mebibits per second) translate into storage quantities over a day, using both the binary (base 2) and decimal (base 10) systems.