Megabytes per day to Gibibits per hour conversion

How to convert megabytes per day to gibibits per hour?

To convert from Megabytes per day (MB/day) to Gibibits per hour (Gibit/h), we need to understand the following relationships:

1. Time Conversion:

   • 1 day = 24 hours

2. Data Size Units:

   • Base 10:

     • 1 Megabyte (MB) = 10^6 bytes (1,000,000 bytes)
     • 1 Gigabit (Gbit) = 10^9 bits (1,000,000,000 bits)

   • Base 2:

     • 1 Megabyte (MB) = 2^20 bytes (1,048,576 bytes)
     • 1 Gibibit (Gibit) = 2^30 bits (1,073,741,824 bits)

Let's walk through the conversion for both base 10 and base 2:

Conversion Using Base 10

1. Convert Megabytes to Bytes:

   $1\, \text{MB/day} = 1 \times 10^6\, \text{Bytes/day}$

2. Convert Bytes to Bits:

   $1\, \text{Byte} = 8\, \text{bits}$

   $1\, \text{MB/day} = 1 \times 10^6 \times 8\, \text{bits/day} = 8 \times 10^6\, \text{bits/day}$

3. Convert Bits per Day to Bits per Hour:

   $\text{Bits per hour} = \dfrac{8 \times 10^6\, \text{bits/day}}{24\, \text{hours/day}} = 333,333.33\, \text{bits/hour}$

4. Convert Bits per Hour to Gigabits per Hour:

   $\text{Gigabits per hour} = \dfrac{333,333.33\, \text{bits/hour}}{10^9} = 0.00033333333\, \text{Gbit/h}$

5. Convert Gigabits to Gibibits:

   • Use the conversion factor where 1 Gigabit = 0.9313225746154785 Gibibits (since if we consider IEEE 1541 standards).

   $\text{Gibibits per hour} = 0.00033333333 \times 0.9313225746154785 = 0.000310441858\, \text{Gibit/h}$

Conversion Using Base 2

1. Convert Megabytes to Bytes:

   $1\, \text{MB/day} = 2^{20}\, \text{Bytes/day} = 1,048,576\, \text{Bytes/day}$

2. Convert Bytes to Bits:

   $1\, \text{Byte} = 8\, \text{bits}$

   $1\, \text{MB/day} = 1,048,576 \times 8\, \text{bits/day} = 8,388,608\, \text{bits/day}$

3. Convert Bits per Day to Bits per Hour:

   $\text{Bits per hour} = \dfrac{8,388,608\, \text{bits/day}}{24\, \text{hours/day}} = 349,525.33\, \text{bits/hour}$

4. Convert Bits per Hour to Gibibits per Hour:

   $\text{Gibibits per hour} = \dfrac{349,525.33\, \text{bits/hour}}{2^{30}} = 0.0003253184\, \text{Gibit/h}$

Real World Examples for Other Quantities of Megabytes per Day

1. 50 MB/day (Base 10):

   • Bits per day: $50\, \text{MB/day} \times 10^6 \times 8 = 4 \times 10^8\, \text{bits/day}$
   • Bits per hour: $\dfrac{4 \times 10^8}{24} = 16,666,666.67\, \text{bits/hour}$
   • Gibibits per hour: $\dfrac{16,666,666.67\, \text{bits/hour}}{10^9} \times 0.9313225746154785 = 0.015522093\, \text{Gibit/h}$

2. 200 MB/day (Base 2):

   • Bytes per day: $200 \times 2^{20} = 209,715,200\, \text{Bytes/day}$
   • Bits per day: $209,715,200 \times 8 = 1,677,721,600\, \text{bits/day}$
   • Gibibits per hour: $\dfrac{1,677,721,600}{24 \times 2^{30}} = 0.0065531\, \text{Gibit/h}$

3. 1 GB/day (~1024 MB/day, Base 2):

   • Bytes per day: $1024 \times 2^{20} = 1,073,741,824\, \text{Bytes/day}$
   • Bits per day: $1,073,741,824 \times 8 = 8,589,934,592\, \text{bits/day}$
   • Gibibits per hour: $\dfrac{8,589,934,592}{24 \times 2^{30}} = 0.333375\, \text{Gibit/h}$

These examples demonstrate how varying amounts of data measured in megabytes per day can be converted into Gibibits per hour using the appropriate base for conversions.