Megabits per day to Gibibits per hour conversion

How to convert megabits per day to gibibits per hour?

To convert 1 Megabit per day (Mb/day) to Gibibits per hour (Gib/hr), you'll first need to understand the conversion factors involved. Here's a step-by-step guide:

Step-by-Step Conversion

1. Convert Megabits to Bits:

   • 1 Megabit = 1,000,000 bits (base 10, SI units)
   • 1 Megabit = 1,048,576 bits (base 2, binary units)

2. Convert Days to Hours:

   • 1 day = 24 hours

3. Apply Conversion to Each Base System:

Base 10 (SI Units)

1. Convert Megabits to Bits: $1 \text{ Megabit} = 1,000,000 \text{ bits}$

2. Calculate Bits per Hour: $\frac{1 \text{ Megabit per day}}{24 \text{ hours}} = \frac{1,000,000 \text{ bits}}{24 \text{ hours}} \approx 41,666.67 \text{ bits per hour}$

3. Convert Bits per Hour to Gibibits per Hour:

   • 1 Gibibit = $2^{30}$ bits = 1,073,741,824 bits (base 2)

   $\frac{41,666.67 \text{ bits per hour}}{1,073,741,824 \text{ bits}} \approx 3.88 \times 10^{-5} \text{ Gibibits per hour}$

Base 2 (Binary Units)

1. Convert Megabits to Bits: $1 \text{ Megabit} = 1,048,576 \text{ bits}$

2. Calculate Bits per Hour: $\frac{1 \text{ Megabit per day}}{24 \text{ hours}} = \frac{1,048,576 \text{ bits}}{24 \text{ hours}} \approx 43,690.67 \text{ bits per hour}$

3. Convert Bits per Hour to Gibibits per Hour:

   • 1 Gibibit = $2^{30}$ bits = 1,073,741,824 bits

   $\frac{43,690.67 \text{ bits per hour}}{1,073,741,824 \text{ bits}} \approx 4.07 \times 10^{-5} \text{ Gibibits per hour}$

Summary of Conversion:

• Base 10 (SI Units):

  • 1 Mb/day ≈ 3.88 x 10^-5 Gib/hr

• Base 2 (Binary Units):

  • 1 Mb/day ≈ 4.07 x 10^-5 Gib/hr

Real-World Examples for Other Quantities of Megabits per Day:

1. 10 Megabits per Day:

   • Base 10: $10 \times 3.88 \times 10^{-5} \approx 3.88 \times 10^{-4} \text{ Gib/hr}$
   • Base 2: $10 \times 4.07 \times 10^{-5} \approx 4.07 \times 10^{-4} \text{ Gib/hr}$

2. 100 Megabits per Day:

   • Base 10: $100 \times 3.88 \times 10^{-5} \approx 3.88 \times 10^{-3} \text{ Gib/hr}$
   • Base 2: $100 \times 4.07 \times 10^{-5} \approx 4.07 \times 10^{-3} \text{ Gib/hr}$

3. 500 Megabits per Day:

   • Base 10: $500 \times 3.88 \times 10^{-5} \approx 1.94 \times 10^{-2} \text{ Gib/hr}$
   • Base 2: $500 \times 4.07 \times 10^{-5} \approx 2.035 \times 10^{-2} \text{ Gib/hr}$

4. 1,000 Megabits per Day:

   • Base 10: $1000 \times 3.88 \times 10^{-5} \approx 3.88 \times 10^{-2} \text{ Gib/hr}$
   • Base 2: $1000 \times 4.07 \times 10^{-5} \approx 4.07 \times 10^{-2} \text{ Gib/hr}$

These conversions provide insight into how different quantities of data measure up in terms of Gibibits per hour, using both base 10 and base 2 systems.