Megabits per second to Gigabits per day conversion

How to convert megabits per second to gigabits per day?

Sure, I'd be happy to explain how to convert Megabits per second (Mbps) to Gigabits per day (Gb/day) and clarify the differences between base 10 and base 2 calculations.

Conversion Approach

1. Base 10 Approach:

   In base 10, common prefixes like "Mega" and "Giga" follow standard decimal values:

   • 1 Mbps = 1,000,000 bits per second.
   • 1 Gbps = 1,000,000,000 bits per second.

2. Base 2 Approach:

   In base 2, commonly used in computing, the prefixes are powers of 2:

   • 1 Mibps (Mebibit per second) = 2^20 bits per second = 1,048,576 bits per second.
   • 1 Gibps (Gibibit per second) = 2^30 bits per second = 1,073,741,824 bits per second.

Step-by-Step Conversion

1. Base 10 (Decimal)

• 1 Mbps = 1,000,000 bits per second.
• There are $60 \times 60 \times 24 = 86,400$ seconds in a day.

Convert 1 Mbps to bits per day: $1,000,000 \, \text{bits/second} \times 86,400 \, \text{seconds/day} = 86,400,000,000 \, \text{bits/day}$

Convert bits to Gigabits: $86,400,000,000 \, \text{bits/day} \div 1,000,000,000 \, \text{bits/Gb} = 86.4 \, \text{Gb/day}$

2. Base 2 (Binary)

• 1 Mbps (base 2) = 1,048,576 bits per second.
• Again, there are 86,400 seconds in a day.

Convert 1 Mibps to bits per day: $1,048,576 \, \text{bits/second} \times 86,400 \, \text{seconds/day} = 90,949,094,400 \, \text{bits/day}$

Convert bits to Gibibits: $90,949,094,400 \, \text{bits/day} \div 1,073,741,824 \, \text{bits/Gib} = 84.71 \, \text{Gib/day}$

Summary of Conversion

• Base 10: 1 Mbps = 86.4 Gb/day.
• Base 2: 1 Mbps = 84.71 Gib/day.

Real-World Examples

Let's take some different quantities of Megabits per second and convert them to Gigabits per day:

1. 10 Mbps:

   • Base 10: $10 \times 86.4 = 864$ Gb/day.
   • Base 2: $10 \times 84.71 = 847.1$ Gib/day.

2. 50 Mbps:

   • Base 10: $50 \times 86.4 = 4320$ Gb/day.
   • Base 2: $50 \times 84.71 = 4235.5$ Gib/day.

3. 100 Mbps:

   • Base 10: $100 \times 86.4 = 8640$ Gb/day.
   • Base 2: $100 \times 84.71 = 8471$ Gib/day.

By understanding these conversions, you can better grasp the data transfer capabilities of different network speeds over longer periods such as days. This is useful for evaluating internet service plans, data usage estimates, and network performance monitoring.