Bytes per hour to Megabits per second conversion

How to convert bytes per hour to megabits per second?

To convert from Bytes per hour to Megabits per second, we need to perform a series of unit conversions. Let's break this down step by step.

1. Convert Bytes to bits: There are 8 bits in a Byte.

2. Convert hours to seconds: There are 3600 seconds in an hour.

3. Combine these to get bits per second: Bits per second (bps) = (Bytes per hour) * 8 bits/Byte / 3600 seconds/hour

4. Convert bits per second to Megabits per second:

   • In base 10: There are $10^6$ bits in a Megabit.
   • In base 2: There are $2^{20}$ bits in a Mebibit (which is often approximated to Megabit depending on context). For simplicity, let's assume 1 Megabit = $2^{20}$ = 1048576 bits.

Base 10 Conversion:

1. Start with 1 Byte/hour.
2. Convert to bits: $1 \text{ Byte/hour} \times 8 \text{ bits/Byte} = 8 \text{ bits/hour}$.
3. Convert to bits per second: $8 \text{ bits/hour} / 3600 \text{ seconds/hour} = 8/3600 \text{ bits/second} \approx 0.00222 \text{ bits/second}$.
4. Convert to Megabits per second: $0.00222 \text{ bits/second} \times (1 \text{ Megabit} / 10^6 \text{ bits}) = 0.00222 / 10^6 \text{ Megabits/second} = 2.22 \times 10^{-9} \text{ Megabits/second}$.

Base 2 Conversion:

1. Start with 1 Byte/hour.
2. Convert to bits: $1 \text{ Byte/hour} \times 8 \text{ bits/Byte} = 8 \text{ bits/hour}$.
3. Convert to bits per second: $8 \text{ bits/hour} / 3600 \text{ seconds/hour} = 8 / 3600 \text{ bits/second} \approx 0.00222 \text{ bits/second}$.
4. Convert to Megabits per second: $0.00222 \text{ bits/second} \times (1 \text{ Megabit} / 2^{20} \text{ bits}) = 0.00222 / 1048576 \text{ Megabits/second} \approx 2.12 \times 10^{-9} \text{ Megabits/second}$.

Real World Examples:

1. 1 Kilobyte per hour (1000 Bytes/hour in base 10 or 1024 Bytes/hour in base 2):

   • Base 10: $1000 \text{ Bytes/hour} \rightarrow 2.22 \times 10^{-6} \text{ Megabits/second}$.
   • Base 2: $1024 \text{ Bytes/hour} \rightarrow 8.67 \times 10^{-6} \text{ Megabits/second}$.

2. 1 Megabyte per hour (1,000,000 Bytes/hour in base 10 or 1,048,576 Bytes/hour in base 2):

   • Base 10: $1,000,000 \text{ Bytes/hour} \rightarrow 2.22 \times 10^{-3} \text{ Megabits/second}$.
   • Base 2: $1,048,576 \text{ Bytes/hour} \rightarrow 8.67 \times 10^{-3} \text{ Megabits/second}$.

3. 1 Gigabyte per hour (1,000,000,000 Bytes/hour in base 10 or 1,073,741,824 Bytes/hour in base 2):

   • Base 10: $1,000,000,000 \text{ Bytes/hour} \rightarrow 2.22 \text{ Megabits/second}$.
   • Base 2: $1,073,741,824 \text{ Bytes/hour} \rightarrow 8.67 \text{ Megabits/second}$.

These calculations illustrate the difference between using base 10 and base 2, which is something to be mindful of in data rate conversions.