Gigabytes per day to Megabits per second conversion

How to convert gigabytes per day to megabits per second?

To convert data from Gigabytes per day (GB/day) to Megabits per second (Mbps), we need to follow a series of steps.

Here’s a step-by-step explanation along with calculations for both base 10 (decimal) and base 2 (binary) units.

Base 10 (decimal) Conversion

1. Understand the Units:
   • 1 Gigabyte (GB) = 1,000 Megabytes (MB)
   • 1 Megabyte (MB) = 1,000 Kilobytes (KB)
   • 1 Kilobyte (KB) = 1,000 Bytes (B)
   • 1 Byte (B) = 8 bits (b)

So, 1 Gigabyte = 1,000,000,000 bytes = 8,000,000,000 bits.

2. Convert Gigabytes per Day to Bits per Day: Since 1 GB = 8,000,000,000 bits,

   • 1 GB/day = 8,000,000,000 bits/day

3. Convert Bits per Day to Bits per Second:

   • There are 24 hours in a day, 60 minutes in an hour, and 60 seconds in a minute.
   • Therefore, there are 24 × 60 × 60 = 86,400 seconds in a day.

   To convert bits per day to bits per second: $\frac{8,000,000,000 \text{ bits}}{86,400 \text{ seconds}} \approx 92,592.59 \text{ bits/second}$

4. Convert Bits per Second to Megabits per Second:

   • 1 Megabit = 1,000,000 bits

   Thus: $\frac{92,592.59 \text{ bits/second}}{1,000,000} \approx 0.0926 \text{ Mbps}$

Base 2 (binary) Conversion

1. Understand the Units:
   • 1 Gigabyte (GB) = 1,024 Megabytes (MB)
   • 1 Megabyte (MB) = 1,024 Kilobytes (KB)
   • 1 Kilobyte (KB) = 1,024 Bytes (B)
   • 1 Byte (B) = 8 bits (b)

So, 1 Gigabyte = 1,024 × 1,024 × 1,024 bytes = 1,073,741,824 bytes = 8,589,934,592 bits.

2. Convert Gigabytes per Day to Bits per Day: Since 1 GB = 8,589,934,592 bits,

   • 1 GB/day = 8,589,934,592 bits/day

3. Convert Bits per Day to Bits per Second: Using the same seconds per day (86,400), $\frac{8,589,934,592 \text{ bits}}{86,400 \text{ seconds}} \approx 99,237.04 \text{ bits/second}$

4. Convert Bits per Second to Megabits per Second:

   • 1 Megabit = 1,024 × 1,024 bits = 1,048,576 bits

   Thus: $\frac{99,237.04 \text{ bits/second}}{1,048,576} \approx 0.0947 \text{ Mbps}$

Real World Examples for Other Quantities

Example 1: 10 GB/day (Base 10)

• Calculation: $10 \times 0.0926 \text{ Mbps} = 0.926 \text{ Mbps}$

Example 2: 50 GB/day (Base 10)

• Calculation: $50 \times 0.0926 \text{ Mbps} = 4.63 \text{ Mbps}$

Example 3: 100 GB/day (Base 10)

• Calculation: $100 \times 0.0926 \text{ Mbps} = 9.26 \text{ Mbps}$

Example 1: 10 GB/day (Base 2)

• Calculation: $10 \times 0.0947 \text{ Mbps} = 0.947 \text{ Mbps}$

Example 2: 50 GB/day (Base 2)

• Calculation: $50 \times 0.0947 \text{ Mbps} = 4.735 \text{ Mbps}$

Example 3: 100 GB/day (Base 2)

• Calculation: $100 \times 0.0947 \text{ Mbps} = 9.47 \text{ Mbps}$

These calculations help in understanding the data transfer rates for different quantities of data expressed in gigabytes per day.