bits per hour to Megabytes per day conversion

How to convert bits per hour to megabytes per day?

To convert data transfer rates from bits per hour (bph) to megabytes per day (MB/day), we need to understand the conversion factors between these units.

Step-by-Step Conversion

1. Convert bits per hour to bits per day:

   • There are 24 hours in a day.
   • Therefore, 1 bph (bits per hour) is: $1 \, \text{bph} \times 24 \, \text{hours/day} = 24 \, \text{bits/day}$

2. Convert bits to bytes:

   • There are 8 bits in a byte.
   • Therefore: $\text{Bytes} = \frac{\text{Bits}}{8}$
   • Applying this to our previous result: $\text{Bytes per day} = \frac{24 \, \text{bits}}{8} = 3 \, \text{bytes/day}$

3. Convert bytes to megabytes:

   • Now the conversion depends on whether we are using base 10 or base 2:

Base 10 (Decimal System)

• 1 Megabyte (MB) = 1,000,000 bytes (10^6 bytes)
• Therefore: $\text{Megabytes per day (base 10)} = \frac{3 \, \text{bytes}}{1,000,000} = 3 \times 10^{-6} \, \text{MB/day}$

Base 2 (Binary System)

• 1 Megabyte (MiB) = 1,048,576 bytes (2^20 bytes)
• Therefore: $\text{Megabytes per day (base 2)} = \frac{3 \, \text{bytes}}{1,048,576} \approx 2.861 \times 10^{-6} \, \text{MiB/day}$

Summary

• Base 10: 1 bph = 3 × 10^-6 MB/day
• Base 2: 1 bph ≈ 2.861 × 10^-6 MiB/day

Real-World Examples for Other Quantities of Bits per Hour

1. Typical Home Internet Connection:

   • Assume a low data rate of 1000 bph.
   • Using base 10: $1000 \, \text{bph} \times 24 \, \text{hours/day} = 24,000 \, \text{bits/day}$ $\text{Bytes per day} = \frac{24,000 \, \text{bits}}{8} = 3,000 \, \text{bytes/day}$ $\text{Megabytes per day} = \frac{3,000 \, \text{bytes}}{1,000,000} = 0.003 \, \text{MB/day} \, (\text{base 10})$

2. High Data Rate Sensor:

   • Assume 1,000,000 bph.
   • Using base 2: $1,000,000 \, \text{bph} \times 24 \, \text{hours/day} = 24,000,000 \, \text{bits/day}$ $\text{Bytes per day} = \frac{24,000,000 \, \text{bits}}{8} = 3,000,000 \, \text{bytes/day}$ $\text{Megabytes per day} = \frac{3,000,000 \, \text{bytes}}{1,048,576} \approx 2.861 \, \text{MiB/day} \, (\text{base 2})$

Through these simple conversions, you can determine data transfer rates in more practical units like megabytes per day, depending on the exact context and the data standards being used (base 10 or base 2).