Bytes per day to Kilobits per second conversion

How to convert bytes per day to kilobits per second?

Converting 1 byte per day to kilobits per second involves several steps. First, let's break down the units and conversion factors involved.

Base 10 (Decimal) Conversion

1. Bytes to Bits:

   • 1 byte = 8 bits

2. Days to Seconds:

   • 1 day = 24 hours
   • 1 hour = 60 minutes
   • 1 minute = 60 seconds
   • Total seconds in a day = 24 * 60 * 60 = 86400 seconds

3. Bits per day to Bits per second:

   • Since there are 86400 seconds in a day, the rate in bits per second is: $\frac{8 \text{ bits}}{86400 \text{ seconds}} \approx 9.26 \times 10^{-5} \text{ bits per second}$

4. Bits per second to Kilobits per second:

   • 1 Kilobit (Kb) = 1000 bits (in base 10)
   • Thus, $9.26 \times 10^{-5} \text{ bits per second} = 9.26 \times 10^{-8} \text{ Kilobits per second}$

Base 2 (Binary) Conversion

1. Bytes to Bits:

   • The same conversion applies, 1 byte = 8 bits

2. Days to Seconds:

   • The calculation remains the same, 1 day = 86400 seconds

3. Bits per day to Bits per second:

   • Again, the same as in base 10, $\frac{8 \text{ bits}}{86400 \text{ seconds}} \approx 9.26 \times 10^{-5} \text{ bits per second}$

4. Bits per second to Kibibits per second:

   • 1 Kibibit (Kib) = 1024 bits (in base 2)
   • Thus, $9.26 \times 10^{-5} \text{ bits per second} = 9.26 \times 10^{-8} \text{ Kibibits per second}$

Now we can summarize the conversions:

• Base 10: 1 byte per day = $9.26 \times 10^{-8}$ Kilobits per second
• Base 2: 1 byte per day = $9.26 \times 10^{-8}$ Kibibits per second

Real World Examples

Let's use the same method to convert some other quantities of Bytes per day.

Example: 1 Megabyte per day (MB/day)

1. Bytes to Bits:

   • 1 Megabyte = 1,000,000 bytes = 8,000,000 bits (base 10)
   • 1 Megabyte = 1,048,576 bytes = 8,388,608 bits (base 2)

2. Bits per day to Bits per second:

   • Base 10: $\frac{8,000,000 \text{ bits}}{86400 \text{ seconds}} \approx 92.59 \text{ bits per second}$
   • Base 2: $\frac{8,388,608 \text{ bits}}{86400 \text{ seconds}} \approx 97.11 \text{ bits per second}$

3. Bits per second to Kilo-/Kibibits per second:

   • Base 10: $92.59 \text{ bits per second} = 0.09259 \text{ Kilobits per second}$
   • Base 2: $97.11 \text{ bits per second} = 0.09484 \text{ Kibibits per second}$

Example: 1 Gigabyte per day (GB/day)

1. Bytes to Bits:

   • 1 Gigabyte = 1,000,000,000 bytes = 8,000,000,000 bits (base 10)
   • 1 Gigabyte = 1,073,741,824 bytes = 8,589,934,592 bits (base 2)

2. Bits per day to Bits per second:

   • Base 10: $\frac{8,000,000,000 \text{ bits}}{86400 \text{ seconds}} \approx 92,592.59 \text{ bits per second}$
   • Base 2: $\frac{8,589,934,592 \text{ bits}}{86400 \text{ seconds}} \approx 99,293.73 \text{ bits per second}$

3. Bits per second to Kilo-/Kibibits per second:

   • Base 10: $92,592.59 \text{ bits per second} = 92.59 \text{ Kilobits per second}$
   • Base 2: $99,293.73 \text{ bits per second} = 97.00 \text{ Kibibits per second}$

These calculations illustrate how to convert bytes per day to kilobits or kibibits per second and showcase the differences between using base 10 and base 2.