bits per second to Kilobytes per second conversion

How to convert bits per second to kilobytes per second?

Sure, I'd be happy to explain how to convert from bits per second (bps) to kilobytes per second (KB/s), and also note the differences between base 10 and base 2.

First, let's clarify a few basic concepts:

1. Bits and Bytes:

   • 1 byte = 8 bits

2. Base 10 vs Base 2:

   • In base 10 nomenclature, "kilo" refers to $10^3$ (1,000), so 1 kilobyte (KB) = 1,000 bytes.
   • In base 2 nomenclature, "kibi" (Ki) refers to $2^{10}$ (1,024), so 1 kibibyte (KiB) = 1,024 bytes.

Conversion Steps in Base 10:

1. Convert bits to bytes:

   • 1 bit per second = 1/8 bytes per second = 0.125 bytes per second.

2. Convert bytes to kilobytes:

   • 1 byte = 1 / 1,000 kilobytes = 0.000125 KB.

3. Combine steps:

   • 1 bps = 0.000125 KB/s.

Conversion Steps in Base 2:

1. Convert bits to bytes:

   • 1 bit per second = 1/8 bytes per second = 0.125 bytes per second.

2. Convert bytes to kibibytes:

   • 1 byte = 1 / 1,024 kibibytes = 0.0001220703125 KiB.

3. Combine steps:

   • 1 bps = 0.0001220703125 KiB/s.

Real-World Examples:

To give you a better understanding, let’s look at some real-world scenarios for higher quantities:

Example 1: Internet Speeds

• 10 Mbps (megabits per second):
  • Base 10: 10 Mbps = 10,000,000 bits/second = 10,000,000 / 8 bytes/second = 1,250,000 bytes/second = 1,250 KB/s.
  • Base 2: 10 Mbps = 10,000,000 bits/second = 10,000,000 / 8 bytes/second = 1,250,000 bytes/second = 1,250,000 / 1,024 KiB/s ≈ 1,220.7 KiB/s.

Example 2: File Downloads

• 100 Mbps:
  • Base 10: 100 Mbps = 100,000,000 bits/second = 100,000,000 / 8 bytes/second = 12,500,000 bytes/second = 12,500 KB/s.
  • Base 2: 100 Mbps = 100,000,000 bits/second = 100,000,000 / 8 bytes/second = 12,500,000 bytes/second = 12,500,000 / 1,024 KiB/s ≈ 12,207 KiB/s.

Example 3: Ethernet Speeds

• 1 Gbps (gigabit per second):
  • Base 10: 1 Gbps = 1,000,000,000 bits/second = 1,000,000,000 / 8 bytes/second = 125,000,000 bytes/second = 125,000 KB/s.
  • Base 2: 1 Gbps = 1,000,000,000 bits/second = 1,000,000,000 / 8 bytes/second = 125,000,000 bytes/second = 125,000,000 / 1,024 KiB/s ≈ 122,070.31 KiB/s.

In summary, the conversion from bits per second to kilobytes per second or kibibytes per second involves first converting bits to bytes (dividing by 8) and then converting bytes to the respective kilobytes (dividing by 1,000 for base 10 KB or by 1,024 for base 2 KiB). The two methods yield slightly different results due to the difference in base definitions for kilo and kibi.