Gibibytes per month to Megabits per hour conversion

How to convert gibibytes per month to megabits per hour?

To convert from Gibibytes per month to Megabits per hour, we need to follow these steps:

1. Understand the units:

   • A Gibibyte (GiB) is $2^{30}$ bytes.
   • A Megabit (Mb) is $10^6$ bits (base 10) or $2^{20}$ bits (base 2).
   • A month is typically considered to be 30 days (for simplicity in these calculations).
   • There are 24 hours in a day.

2. Convert from Gibibytes to bits:

   • For base 2: $1 \text{ GiB} = 2^{30} \text{ bytes}$ and each byte is 8 bits. $1 \text{ GiB} = 2^{30} \times 8 \text{ bits} = 2^{33} \text{ bits}$
   • For base 10: $1 \text{ GiB} = 2^{30} \text{ bytes}$ and each byte is 8 bits. $1 \text{ GiB} = 2^{30} \times 8 \text{ bits} = 8,589,934,592 \text{ bits}$

3. Convert per month to per hour:

   • There are 30 days and 24 hours/day in a month: $1 \text{ month} = 30 \times 24 \text{ hours} = 720 \text{ hours}$

4. Convert from bits to Megabits:

   • Megabits in base 2: $1 \text{ Megabit} = 2^{20} \text{ bits}$
   • Megabits in base 10: $1 \text{ Megabit} = 10^6 \text{ bits}$

Now, let's perform the conversions both ways:

Base 2 Conversion:

1. Gibibytes to bits: $1 \text{ GiB} = 2^{33} \text{ bits}$

2. Bits per hour: $\text{Bits per hour} = \frac{2^{33} \text{ bits}}{720 \text{ hours}} = \frac{8,589,934,592 \text{ bits}}{720} \approx 11,930,485 \text{ bits/hour}$

3. Bits per hour to Megabits per hour (base 2): $\text{Megabits per hour} = \frac{11,930,485 \text{ bits/hour}}{2^{20}} \approx 11.38 \text{ Megabits per hour}$

Base 10 Conversion:

1. Gibibytes to bits: $1 \text{ GiB} = 8,589,934,592 \text{ bits}$

2. Bits per hour: $\text{Bits per hour} = \frac{8,589,934,592 \text{ bits}}{720 \text{ hours}} \approx 11,930,485 \text{ bits/hour}$

3. Bits per hour to Megabits per hour (base 10): $\text{Megabits per hour} = \frac{11,930,485 \text{ bits/hour}}{10^6} \approx 11.93 \text{ Megabits per hour}$

Real World Examples:

50 GiB per month:

• Base 2:

  • Bits per month: $50 \times 2^{33} = 50 \times 8,589,934,592 = 429,496,729,600 \text{ bits}$
  • Bits per hour: $\frac{429,496,729,600}{720} \approx 596,524,626 \text{ bits/hour}$
  • Megabits per hour (base 2): $\frac{596,524,626}{2^{20}} \approx 568.82 \text{ Megabits/hour}$

• Base 10:

  • Bits per month: $50 \times 8,589,934,592 = 429,496,729,600 \text{ bits}$
  • Bits per hour: $\frac{429,496,729,600}{720} \approx 596,524,626 \text{ bits/hour}$
  • Megabits per hour (base 10): $\frac{596,524,626}{10^6} = 596.52 \text{ Megabits/hour}$

100 GiB per month:

• Base 2:

  • Bits per month: $100 \times 2^{33} = 858,993,459,200 \text{ bits}$
  • Bits per hour: $\frac{858,993,459,200}{720} \approx 1,193,048,252 \text{ bits/hour}$
  • Megabits per hour (base 2): $\frac{1,193,048,252}{2^{20}} \approx 1,137.64 \text{ Megabits/hour}$

• Base 10:

  • Bits per month: $100 \times 8,589,934,592 = 858,993,459,200 \text{ bits}$
  • Bits per hour: $\frac{858,993,459,200}{720} \approx 1,193,048,252 \text{ bits/hour}$
  • Megabits per hour (base 10): $\frac{1,193,048,252}{10^6} = 1,193.05 \text{ Megabits/hour}$

These calculations help demonstrate how to convert data transfer rates using both base 2 and base 10 systems.