Megabits per second to Gibibits per day conversion

How to convert megabits per second to gibibits per day?

Sure, let's break down the conversion from Megabits per second (Mbps) to Gibibits per day (Gib/d). To understand this, we need to go through the following steps:

Base 10 Conversion

Step 1: Convert Megabits to Gigabits

In the decimal (base 10) system:

• 1 Megabit (Mb) = 1,000,000 bits = 1 x 10^6 bits.
• 1 Gigabit (Gb) = 1,000,000,000 bits = 1 x 10^9 bits.

Hence, 1 Megabit = 1 x 10^-3 Gigabits.

Step 2: Convert Megabits per second to Gigabits per second

Since 1 Megabit = 0.001 Gigabits:

• 1 Mbps = 0.001 Gbps.

Step 3: Calculate number of seconds in a day

• 1 day = 24 hours.
• 1 hour = 60 minutes.
• 1 minute = 60 seconds.
• Therefore, 1 day = 24 * 60 * 60 = 86,400 seconds.

Step 4: Convert Mbps to Gigabits per day

• 1 Mbps = 0.001 Gbps.
• In one day, the data transferred will be: $0.001 \text{ Gbps} \times 86,400 \text{ seconds} = 86.4 \text{ Gigabits per day}$.

Step 5: Convert Gigabits per day to Gibibits per day

In the binary (base 2) system:

• 1 Gigabit (Gb) = 1,000,000,000 bits.
• 1 Gibibit (Gib) = 2^30 bits = 1,073,741,824 bits.

Thus, $\text{Gibibits per day} = \frac{\text{Gigabits per day}}{1,073,741,824 / 10^9}$ $\text{Gibibits per day} = \frac{86.4}{1.073741824} = 80.485 \text{ Gib/d}$

Base 2 Conversion (Binary)

Step 1: Calculate number of seconds in a day

This remains the same: $1 \text{ day} = 86,400 \text{ seconds}$

Step 2: Convert Megabits per second to bits per second

• 1 Megabit = 2^20 bits (1,048,576 bits).

Step 3: Calculate total bits per day

$1 \text{ Mbps} = 1,048,576 \text{ bits per second}$ $1 \text{ Mbps} \times 86,400 \text{ seconds} = 90,946,560,000 \text{ bits per day}$

Step 4: Convert bits per day to Gibibits per day

• 1 Gibibit = 2^30 bits (1,073,741,824 bits). $\text{Gibibits per day} = \frac{90,946,560,000 \text{ bits}}{1,073,741,824 \text{ bits per Gib}} = 84.623 \text{ Gib}$

Summary:

• Base 10 Conversion: 1 Mbps = 86.4 Gigabits per day ≈ 80.485 Gibibits per day.
• Base 2 Conversion: 1 Mbps ≈ 84.623 Gibibits per day.

Real-world Examples:

1. 10 Mbps:

   • Base 10: 864 Gigabits/day ≈ 804.85 Gib/day.
   • Base 2: 846.23 Gib/day.

2. 100 Mbps:

   • Base 10: 8640 Gigabits/day ≈ 8048.5 Gib/day.
   • Base 2: 8462.3 Gib/day.

3. 1000 Mbps (1 Gbps):

   • Base 10: 86,400 Gigabits/day ≈ 80,485 Gib/day.
   • Base 2: 84,623 Gib/day.

These calculations show how Mbps can be converted to Gib/d in both base 10 and base 2, with real-world scenarios illustrating practical data transfer rates.