Megabytes per day to Terabits per hour conversion

How to convert megabytes per day to terabits per hour?

To convert from Megabytes per day (MB/day) to Terabits per hour (Tb/hr), you need to navigate between units of data (Megabytes to Terabits) and units of time (days to hours). The conversion process differs slightly depending on whether you use base 10 (decimal) or base 2 (binary) units for data measurement.

Base 10 (Decimal) Calculations

In the decimal system:

• 1 Megabyte (MB) = 10^6 Bytes
• 1 Terabit (Tb) = 10^12 Bits
• 1 Byte = 8 Bits

Step-by-Step Conversion:

1. Convert 1 MB to Bits:
   $1 \text{ MB} = 1 \times 10^6 \text{ Bytes} \times 8 = 8 \times 10^6 \text{ Bits}$

2. Convert Bits to Terabits:
   $8 \times 10^6 \text{ Bits} = \frac{8 \times 10^6}{10^{12}} \text{ Terabits}$
   $= 8 \times 10^{-6} \text{ Terabits}$

3. Convert Days to Hours:
   $1 \text{ day} = 24 \text{ hours}$

4. Calculate Terabits per Hour:
   $\text{Terabits per hour} = \frac{8 \times 10^{-6} \text{ Terabits}}{24 \text{ hours}}$
   $= \frac{8 \times 10^{-6}}{24} \text{ Tb/hr}$
   $\approx 3.33 \times 10^{-7} \text{ Tb/hr}$

Base 2 (Binary) Calculations

In the binary (computer science) system:

• 1 Megabyte (MB) = 2^20 Bytes
• 1 Terabit (Tb) = 2^40 Bits
• 1 Byte = 8 Bits

Step-by-Step Conversion:

1. Convert 1 MB to Bits:
   $1 \text{ MB} = 2^{20} \text{ Bytes} \times 8 = 8 \times 2^{20} \text{ Bits}$
   $= 2^{23} \text{ Bits}$

2. Convert Bits to Terabits:
   $2^{23} \text{ Bits} = \frac{2^{23}}{2^{40}} \text{ Terabits}$
   $= 2^{-17} \text{ Terabits}$

3. Convert Days to Hours:
   $1 \text{ day} = 24 \text{ hours}$

4. Calculate Terabits per Hour:
   $\text{Terabits per hour} = \frac{2^{-17} \text{ Terabits}}{24 \text{ hours}}$
   $= \frac{1}{24 \times 2^{17}} \text{ Tb/hr}$
   $\approx 4.77 \times 10^{-8} \text{ Tb/hr}$

Real-World Examples:

1. Daily Email Traffic: A mid-sized company generates around 500 MB of email data per day.

   • Base 10: 500 MB/day = $500 \times 3.33 \times 10^{-7}$ Tb/hr ≈ 1.67 \times 10^{-4} Tb/hr.
   • Base 2: 500 MB/day = $500 \times 4.77 \times 10^{-8}$ Tb/hr ≈ 2.39 \times 10^{-5} Tb/hr.

2. Website Traffic: A popular website might have 5 GB/day of data traffic.

   • Base 10: 5 GB/day = $5000 \times 3.33 \times 10^{-7}$ Tb/hr ≈ 1.67 \times 10^{-3} Tb/hr.
   • Base 2: 5 GB/day = $5000 \times 4.77 \times 10^{-8}$ Tb/hr ≈ 2.39 \times 10^{-4} Tb/hr.

3. Streaming Service: An average streaming service might transmit around 100 GB/day.

   • Base 10: 100 GB/day = $100000 \times 3.33 \times 10^{-7}$ Tb/hr ≈ 3.33 \times 10^{-2} Tb/hr.
   • Base 2: 100 GB/day = $100000 \times 4.77 \times 10^{-8}$ Tb/hr ≈ 4.77 \times 10^{-3} Tb/hr.