bits per minute to Terabits per day conversion

How to convert bits per minute to terabits per day?

Sure, let's break down the conversion from bits per minute to Terabits per day step-by-step.

Conversion Procedure

1. Convert minutes to days:

   • There are 60 minutes in an hour.
   • There are 24 hours in a day.
   • Therefore, there are $60 \times 24 = 1440$ minutes in a day.

2. Convert bits per minute to bits per day:

   • If you have 1 bit per minute, over a day you would have $1 \text{ bit/minute} \times 1440 \text{ minutes/day} = 1440 \text{ bits/day}$.

3. Convert bits to Terabits:

   • Base 10 (Decimal):

     • 1 Terabit $= 10^{12}$ bits.
     • Therefore, $1440 \text{ bits/day} / 10^{12} \text{ bits/Terabit} = 1.44 \times 10^{-9} \text{ Terabits/day}$.

   • Base 2 (Binary):

     • 1 Terabit $= 2^{40}$ bits.
     • Therefore, $1440 \text{ bits/day} / 2^{40} \text{ bits/Terabit} \approx 1.307 \times 10^{-9} \text{ Terabits/day}$.

Summary

• Base 10 (Decimal): 1 bit per minute = $1.44 \times 10^{-9}$ Terabits per day.
• Base 2 (Binary): 1 bit per minute = $1.307 \times 10^{-9}$ Terabits per day.

Real World Examples

To give you an idea of other quantities of bits per minute, let's consider some examples:

1. 64 kbps (kilobits per second) Internet connection:

   • $64,000 \text{ bits/second} \times 60 \text{ seconds/minute} = 3,840,000 \text{ bits/minute}$
   • Convert to bits per day: $3,840,000 \text{ bits/minute} \times 1440 \text{ minutes/day} = 5,529,600,000 \text{ bits/day}$
   • Convert to Terabits:
     • Base 10: $5.5296 \times 10^9 \text{ bits/day} / 10^{12} = 5.5296 \times 10^{-3} \text{ Terabits/day}$
     • Base 2: $5.5296 \times 10^9 \text{ bits/day} / 2^{40} \approx 5.026 \times 10^{-3} \text{ Terabits/day}$

2. Streaming video at 5 Mbps (megabits per second):

   • $5,000,000 \text{ bits/second} \times 60 \text{ seconds/minute} = 300,000,000 \text{ bits/minute}$
   • Convert to bits per day: $300,000,000 \text{ bits/minute} \times 1440 \text{ minutes/day} = 432,000,000,000 \text{ bits/day}$
   • Convert to Terabits:
     • Base 10: $432 \times 10^9 \text{ bits/day} / 10^{12} = 0.432 \text{ Terabits/day}$
     • Base 2: $432 \times 10^9 \text{ bits/day} / 2^{40} \approx 0.39 \text{ Terabits/day}$

3. 10 Gbps (Gigabits per second) data center network traffic:

   • $10,000,000,000 \text{ bits/second} \times 60 \text{ seconds/minute} = 600,000,000,000 \text{ bits/minute}$
   • Convert to bits per day: $600,000,000,000 \text{ bits/minute} \times 1440 \text{ minutes/day} = 864,000,000,000,000 \text{ bits/day}$
   • Convert to Terabits:
     • Base 10: $864 \times 10^{12} \text{ bits/day} / 10^{12} = 864 \text{ Terabits/day}$
     • Base 2: $864 \times 10^{12} \text{ bits/day} / 2^{40} \approx 786.43 \text{ Terabits/day}$

These examples demonstrate how different data rates can translate to significant amounts of data transferred over a day, expressed in Terabits.