bits per hour to Mebibytes per hour conversion

How to convert bits per hour to mebibytes per hour?

Converting bits per hour (bph) to Mebibytes per hour (MiB/hr) involves understanding both binary (base 2) and decimal (base 10) conversions. Here's how you can do the conversion for both bases:

Base 2 (Binary)

1. Base Units:

   • 1 Byte (B) = 8 bits (b)
   • 1 Kibibyte (KiB) = 1024 Bytes (B)
   • 1 Mebibyte (MiB) = 1024 Kibibytes (KiB)

2. Conversion from Bits to Bytes:

   • 1 bit = 1/8 Bytes

3. Conversion from Bytes to Mebibytes:

   • 1 Byte = 1/(8 * 1024 * 1024) MiB

Steps:

1. Start with 1 bit per hour.
2. Convert to Bytes: $\frac{1 \text{ bit}}{8} = 0.125 \text{ Bytes}$
3. Convert to MiB: $0.125 \text{ Bytes} \times \frac{1 \text{ MiB}}{1024 \times 1024 \text{ Bytes}} = 0.125 \times \frac{1}{1048576} \text{ MiB}$

Final Calculation for Base 2: $0.125 \times \frac{1}{1048576} \text{ MiB} = \frac{0.125}{1048576} \text{ MiB} = 1.19209290 \times 10^{-7} \text{ MiB/hr}$

Base 10 (Decimal)

1. Base Units:

   • 1 Byte (B) = 8 bits (b)
   • 1 Kilobyte (KB) = 1000 Bytes (B)
   • 1 Megabyte (MB) = 1000 Kilobytes (KB)

2. Conversion from Bits to Bytes:

   • 1 bit = 1/8 Bytes

3. Conversion from Bytes to Megabytes:

   • 1 Byte = 1/(8 * 1000 * 1000) MB

Steps:

1. Start with 1 bit per hour.
2. Convert to Bytes: $\frac{1 \text{ bit}}{8} = 0.125 \text{ Bytes}$
3. Convert to MB: $0.125 \text{ Bytes} \times \frac{1 \text{ MB}}{1000 \times 1000 \text{ Bytes}} = 0.125 \times \frac{1}{1000000} \text{ MB}$

Final Calculation for Base 10: $0.125 \times \frac{1}{1000000} \text{ MB} = \frac{0.125}{1000000} \text{ MB} = 1.25 \times 10^{-7} \text{ MB/hr}$

Real-World Examples for Other Quantities of Bits per Hour

1. Internet Connection Speed:

   • A slow internet connection might be around 64 Kilobits per second (Kbps).
     • Conversion: $64 \text{ Kbps} \times 3600 \text{ seconds/hour} = 230,400 \text{ Kbps/hr}$.
     • In bits: $230,400 \times 1000 = 230,400,000 \text{ bits/hr}$.
     • Base 2 (MiB/hr): $230,400,000 \div (8 \times 1024 \times 1024) \approx 27.5 \text{ MiB/hr}$.

2. File Download Size:

   • Downloading a 1 Gigabyte file at a speed of 1 Megabit per second.
     • Conversion: $1 \text{ Mbps} \times 3600 \text{ seconds/hour} = 3,600 \text{ Mbps/hr}$.
     • In bits: $3,600,000,000 \text{ bits/hr}$.
     • Base 2 (MiB/hr): $3,600,000,000 \div (8 \times 1024 \times 1024) \approx 429.69 \text{ MiB/hr}$.

3. Video Streaming:

   • Streaming a video at 5 Megabits per second.
     • Conversion: $5 \text{ Mbps} \times 3600 \text{ seconds/hour} = 18,000 \text{ Mbps/hr}$.
     • In bits: $18,000,000,000 \text{ bits/hr}$.
     • Base 2 (MiB/hr): $18,000,000,000 \div (8 \times 1024 \times 1024) \approx 2145.77 \text{ MiB/hr}$.

Each of these examples uses base 2 (binary). If you need the base 10 (decimal) conversions, you simply replace $1024$ with $1000$ in the respective calculations for converting Bytes to Megabytes (MB).