Megabytes per hour to Terabits per second conversion

How to convert megabytes per hour to terabits per second?

To convert from Megabytes per hour (MB/hr) to Terabits per second (Tbps), we need to follow a step-by-step process to ensure all units are properly converted.

Step-by-Step Conversion for Base 10 (Decimal System):

1. Convert hours to seconds:

   • 1 hour = 3600 seconds.

2. Convert Megabytes to bytes:

   • In the base 10 system, 1 Megabyte (MB) = 1,000,000 bytes (1 MB = 10^6 bytes).

3. Convert bytes to bits:

   • 1 byte = 8 bits.

4. Combine the above conversions:

   • 1 MB/hr = 1,000,000 bytes/hour.
   • Since there are 3600 seconds in an hour:
     • $\frac{1,000,000 \text{ bytes}}{3600 \text{ seconds}} \approx 277.78 \text{ bytes/second}$.

5. Convert bytes/second to bits/second:

   • $277.78 \text{ bytes/second} \times 8 \text{ bits/byte} \approx 2,222.22 \text{ bits/second}$.

6. Convert bits/second to Terabits/second:

   • 1 Terabit (Tb) = 10^12 bits.
   • $\frac{2,222.22 \text{ bits/second}}{10^{12}} \approx 2.22 \times 10^{-9} \text{ Tbps}$.

So, 1 Megabyte per hour is approximately $2.22 \times 10^{-9}$ Terabits per second in the base 10 system.

Step-by-Step Conversion for Base 2 (Binary System):

1. Convert hours to seconds:

   • 1 hour = 3600 seconds.

2. Convert Megabytes to bytes:

   • In the base 2 system, 1 Megabyte (MB) = 1,048,576 bytes (1 MB = $2^{20}$ bytes).

3. Convert bytes to bits:

   • 1 byte = 8 bits.

4. Combine the above conversions:

   • 1 MB/hr = 1,048,576 bytes/hour.
   • Since there are 3600 seconds in an hour:
     • $\frac{1,048,576 \text{ bytes}}{3600 \text{ seconds}} \approx 291.27 \text{ bytes/second}$.

5. Convert bytes/second to bits/second:

   • $291.27 \text{ bytes/second} \times 8 \approx 2,330.16 \text{ bits/second}$.

6. Convert bits/second to Terabits/second:

   • 1 Terabit (Tb) = $2^{40}$ bits = 1,099,511,627,776 bits.
   • $\frac{2,330.16 \text{ bits/second}}{2^{40}} \\approx 2.12 \times 10^{-9} \text{ Tbps}$.

So, 1 Megabyte per hour is approximately $2.12 \times 10^{-9}$ Terabits per second in the base 2 system.

Real World Examples:

1. Streaming Music:

   • Streaming music at a typical 320 kbps (kilobits per second) rate consumes approximately 144 MB per hour.
   • Converting 144 MB/hr to Tbps in the base 10 system:
     • $144 \text{ MB/hr} = 144 \times 2.22 \times 10^{-9} \text{ Tbps} \approx 3.20 \times 10^{-7} \text{ Tbps}$.
   • In the base 2 system:
     • $144 \text{ MB/hr} = 144 \times 2.12 \times 10^{-9} \text{ Tbps} \approx 3.05 \times 10^{-7} \text{ Tbps}$.

2. Watching HD Video:

   • Streaming HD video at 3 Mbps (megabits per second) consumes about 1,350 MB per hour.
   • Converting 1,350 MB/hr to Tbps in the base 10 system:
     • $1,350 \text{ MB/hr} = 1,350 \times 2.22 \times 10^{-9} \text{ Tbps} \approx 2.997 \times 10^{-6} \text{ Tbps}$.
   • In the base 2 system:
     • $1,350 \text{ MB/hr} = 1,350 \times 2.12 \times 10^{-9} \text{ Tbps} \approx 2.87 \times 10^{-6} \text{ Tbps}$.

3. Data Backup:

   • An enterprise backup that transfers data at 50 GB per hour.
   • Converting 50 GB/hr to Mb/hr (50 GB = 50,000 MB):
     • $50,000 \text{ MB/hr}$.
   • Converting 50,000 MB/hr to Tbps in the base 10 system:
     • $50,000 \text{ MB/hr} = 50,000 \times 2.22 \times 10^{-9} \text{ Tbps} \approx 1.11 \times 10^{-4} \text{ Tbps}$.
   • In the base 2 system:
     • $50,000 \text{ MB/hr} = 50,000 \times 2.12 \times 10^{-9} \text{ Tbps} \approx 1.06 \times 10^{-4} \text{ Tbps}$.

These examples show that even relatively low data transfer rates per hour convert to very small values in Terabits per second, demonstrating the vast difference in the scales of these units.