Megabits per second to bits per hour conversion

How to convert megabits per second to bits per hour?

To convert 1 Megabit per second (Mbps) to bits per hour, we need to follow a few steps and ensure we understand both base 10 and base 2 interpretations. First, let's clarify the difference between the two bases.

Base 10 (Decimal System)

In the decimal system, 1 Megabit equals $10^6$ bits (1,000,000 bits).

Base 2 (Binary System)

In the binary system, 1 Megabit equals $2^{20}$ bits (1,048,576 bits).

Conversion Process

1. Determine the number of seconds in an hour: There are 60 seconds in a minute and 60 minutes in an hour. Therefore, the number of seconds in an hour is: $60 \times 60 = 3600 \text{ seconds}$

2. Calculate bits per hour for both base 10 and base 2:

Base 10:

• 1 Megabit per second (Mbps) = $10^6$ bits per second.
• To find bits per hour: $10^6 \text{ bits/second} \times 3600 \text{ seconds/hour} = 3,600,000,000 \text{ bits/hour}$

Base 2:

• 1 Megabit per second (Mbps) = $2^{20}$ bits per second.
• To find bits per hour: $2^{20} \text{ bits/second} \times 3600 \text{ seconds/hour} = 3,773,941,760 \text{ bits/hour}$

Real-world Examples

Let's consider some real-world examples for other quantities of Megabits per second:

1. 5 Mbps (Base 10):

   • Bits per hour: $5 \times 10^6 \text{ bits/second} \times 3600 \text{ seconds/hour} = 18,000,000,000 \text{ bits/hour}$

2. 10 Mbps (Base 2):

   • Bits per hour: $10 \times 2^{20} \text{ bits/second} \times 3600 \text{ seconds/hour} = 37,739,417,600 \text{ bits/hour}$

3. 50 Mbps (Base 10):

   • Bits per hour: $50 \times 10^6 \text{ bits/second} \times 3600 \text{ seconds/hour} = 180,000,000,000 \text{ bits/hour}$

4. 100 Mbps (Base 2):

   • Bits per hour: $100 \times 2^{20} \text{ bits/second} \times 3600 \text{ seconds/hour} = 377,394,176,000 \text{ bits/hour}$

These examples show how to convert Mbps to bits per hour in both the decimal and binary systems and provide an insight into how significant the difference can be depending on the base considered.