Kilobits per day to Megabits per second conversion

How to convert kilobits per day to megabits per second?

To convert 1 Kilobit per day (Kb/day) to Megabits per second (Mbps), we need to go through the following steps:

1. Convert Kilobits to Bits:

   • 1 Kilobit (Kb) = 1,000 bits (b) in base 10.
   • 1 Kilobit (Kb) = 1,024 bits (b) in base 2.

2. Convert days to seconds:

   • 1 day = 24 hours
   • 1 hour = 60 minutes
   • 1 minute = 60 seconds
   • Therefore, 1 day = 24 * 60 * 60 = 86,400 seconds

3. Find the Data Transfer Rate in bits per second (bps):

   • For base 10: $\text{bps} = \frac{1,000 \text{ bits}}{86,400 \text{ seconds}}$
   • For base 2: $\text{bps} = \frac{1,024 \text{ bits}}{86,400 \text{ seconds}}$

4. Convert from bits per second to Megabits per second:

   • 1 Megabit (Mb) = 1,000,000 bits in base 10.
   • 1 Megabit (Mb) = 1,048,576 bits in base 2.

Now let's do the calculations:

Base 10 Calculation:

1. Bits per second: $\text{bps} = \frac{1,000 \text{ bits}}{86,400 \text{ seconds}} \approx 0.01157 \text{ bps}$

2. Megabits per second: $\text{Mbps} = \frac{0.01157 \text{ bps}}{1,000,000 \text{ bits per Mbps}} \approx 1.157 \times 10^{-8} \text{ Mbps}$

Base 2 Calculation:

1. Bits per second: $\text{bps} = \frac{1,024 \text{ bits}}{86,400 \text{ seconds}} \approx 0.01185 \text{ bps}$

2. Megabits per second: $\text{Mbps} = \frac{0.01185 \text{ bps}}{1,048,576 \text{ bits per Mbps}} \approx 1.129 \times 10^{-8} \text{ Mbps}$

Real World Examples:

10 Kilobits per day:

• Base 10: $\approx 1.157 \times 10^{-7} \text{ Mbps}$
• Base 2: $\approx 1.129 \times 10^{-7} \text{ Mbps}$

1 Megabit per day:

• Convert 1 Megabit to Kilobits (1 Megabit = 1,000 Kilobits in base 10, or 1,024 Kilobits in base 2):
  • Base 10: $1,000 \text{ Kb/day} \approx 1.157 \times 10^{-5} \text{ Mbps}$
  • Base 2: $1,024 \text{ Kb/day} \approx 1.129 \times 10^{-5} \text{ Mbps}$

1 Gigabit per day:

• Convert 1 Gigabit to Kilobits (1 Gigabit = 1,000,000 Kilobits in base 10, or 1,048,576 Kilobits in base 2):
  • Base 10: $1,000,000 \text{ Kb/day} \approx 1.157 \times 10^{-2} \text{ Mbps}$
  • Base 2: $1,048,576 \text{ Kb/day} \approx 1.129 \times 10^{-2} \text{ Mbps}$

1 Terabit per day:

• Convert 1 Terabit to Kilobits (1 Terabit = 1,000,000,000 Kilobits in base 10, or 1,073,741,824 Kilobits in base 2):
  • Base 10: $1,000,000,000 \text{ Kb/day} \approx 11.57 \text{ Mbps}$
  • Base 2: $1,073,741,824 \text{ Kb/day} \approx 11.29 \text{ Mbps}$

These conversions give you an idea of how small 1 Kilobit per day is when expressed in Megabits per second, and show the difference in conversion between base 10 and base 2.