Mebibits per day to Gigabytes per hour conversion

How to convert mebibits per day to gigabytes per hour?

Converting data transfer rates from Mebibits per day to Gigabytes per hour involves several steps, including converting between units of time and data size. We need to be careful about whether to use base 2 (binary) or base 10 (decimal) because this can affect the result. Let's go through both conversions.

Definitions and Assumptions

1. Mebibit (Mibit):
   • 1 Mebibit = $2^{20}$ bits = 1,048,576 bits.
2. Gigabyte (GB) in base 2:
   • 1 Gigabyte (GB) = $2^{30}$ bytes = 1,073,741,824 bytes.
   • 1 byte = 8 bits, so 1 GB = 1,073,741,824 bytes × 8 bits/byte = 8,589,934,592 bits.
3. Gigabyte (GB) in base 10:
   • 1 Gigabyte (GB) = $10^9$ bytes = 1,000,000,000 bytes.
   • 1 byte = 8 bits, so 1 GB = 1,000,000,000 bytes × 8 bits/byte = 8,000,000,000 bits.

Step-by-Step Conversion

1. Convert Mebibits per Day to Bits per Day

• 1 Mibit = 1,048,576 bits.
• So, 1 Mibit/day = 1,048,576 bits/day.

2. Convert Bits per Day to Bits per Hour

• There are 24 hours in a day.
• So, bits/hour = $\frac{1,048,576 \text{ bits}}{24 \text{ hours}} \approx 43,690.67 \text{ bits/hour}$.

3. Convert Bits per Hour to Gigabytes per Hour

For base 2:

• 1 Gigabyte (base 2) = 8,589,934,592 bits.
• Gigabytes/hour = $\frac{43,690.67 \text{ bits}}{8,589,934,592 \text{ bits/GB}} \approx 5.088 \times 10^{-6} \text{ GB/hour}$.

For base 10:

• 1 Gigabyte (base 10) = 8,000,000,000 bits.
• Gigabytes/hour = $\frac{43,690.67 \text{ bits}}{8,000,000,000 \text{ bits/GB}} \approx 5.461 \times 10^{-6} \text{ GB/hour}$.

Real-World Examples

1. Streaming Video

• Assume a typical streaming video bitrate is 4 Mebibits per second (Mbps).
• Converting 4 Mbps to Mebibits per day:
  • 4 Mbps × 60 seconds/min × 60 min/hour × 24 hours/day = 345,600 Mebibits/day.
• Converting this to Gigabytes per hour:
  • Base 2: $345,600 \text{ Mibit/day} \approx 1.75 \text{ GB/hour}$.
  • Base 10: $345,600 \text{ Mibit/day} \approx 1.80 \text{ GB/hour}$.

2. Data Download for Backup Systems

• Suppose a backup system transfers data at a rate of 100 Mebibits per hour.
• Converting 100 Mbps to Mebibits per day:
  • 100 Mbps × 60 min/hour × 24 hours/day = 144,000 Mebibits/day.
• Converting this to Gigabytes per hour:
  • Base 2: $144,000 \text{ Mibit/day} \approx 0.734 \text{ GB/hour}$.
  • Base 10: $144,000 \text{ Mibit/day} \approx 0.760 \text{ GB/hour}$.

These calculations allow you to translate between data units and time units practically, capturing the differences where base 2 and base 10 measurements lead to slight variations in the outcomes.