bits per second to Mebibits per hour conversion

How to convert bits per second to mebibits per hour?

Sure! To convert 1 bit per second (bps) to Mebibits per hour (Mib/hr), we need to perform several steps since we are converting both the unit of data (bits to Mebibits) and the unit of time (seconds to hours).

Firstly, let's look at the definitions:

• 1 Mebibit (Mib) = 2^20 bits (base 2 measurement)
• 1 Megabit (Mb) = 10^6 bits (base 10 measurement)
• 1 hour = 3600 seconds

Base 2 (Mebibit) Conversion:

1. Start with 1 bit per second (bps).

2. To find out how many bits this corresponds to in one hour: $1 \, \text{bit/sec} \times 3600 \, \text{sec} = 3600 \, \text{bits/hour}$

3. Convert bits to Mebibits (Mib): $\frac{3600 \, \text{bits}}{2^{20} \, \text{bits/Mib}} = \frac{3600}{1048576} \, \text{Mib} \approx 0.0034332 \, \text{Mib/hour}$

So, $1 \, \text{bps}$ is approximately $0.0034332 \, \text{Mib/hour}$.

Base 10 (Megabit) Conversion:

1. Start with 1 bit per second (bps).

2. To find out how many bits this corresponds to in one hour: $1 \, \text{bit/sec} \times 3600 \, \text{sec} = 3600 \, \text{bits/hour}$

3. Convert bits to Megabits (Mb): $\frac{3600 \, \text{bits}}{10^6 \, \text{bits/Mb}} = \frac{3600}{1000000} \, \text{Mb} = 0.0036 \, \text{Mb/hour}$

So, $1 \, \text{bps}$ is equal to $0.0036 \, \text{Mb/hour}$.

Real-World Examples:

Let's look at some more practical data rates:

Example 1: 1 Mbps (Megabit per second)

1. Base 2: $1 \, \text{Mbps} = \frac{1 \times 10^6 \, \text{bits/sec}}{2^{20} \, \text{bits/Mib}} \approx 0.9537 \, \text{Mib/sec}$ Over an hour: $0.9537 \, \text{Mib/sec} \times 3600 \, \text{sec} = 3433.32 \, \text{Mib/hour}$

2. Base 10: $1 \, \text{Mbps} = \frac{1 \times 10^6 \, \text{bits/sec}}{10^6 \, \text{bits/Mb}} = 1 \, \text{Mb/sec}$ Over an hour: $1 \, \text{Mb/sec} \times 3600 \, \text{sec} = 3600 \, \text{Mb/hour}$

Example 2: Typical home internet speed (e.g., 100 Mbps)

1. Base 2: $100 \, \text{Mbps} = \frac{100 \times 10^6 \, \text{bits/sec}}{2^{20} \, \text{bits/Mib}} \approx 95.37 \, \text{Mib/sec}$ Over an hour: $95.37 \, \text{Mib/sec} \times 3600 \, \text{sec} = 343332 \, \text{Mib/hour}$

2. Base 10: $100 \, \text{Mbps} = \frac{100 \times 10^6 \, \text{bits/sec}}{10^6 \, \text{bits/Mb}} = 100 \, \text{Mb/sec}$ Over an hour: $100 \, \text{Mb/sec} \times 3600 \, \text{sec} = 360000 \, \text{Mb/hour}$

These examples demonstrate how data rates scale up and how they are measured in both base 2 (binary) and base 10 (decimal) notations.