What is the Binary System?

The binary system is a numerical system that functions virtually identically to the decimal number system that people are likely more familiar with. While the decimal number system uses the number 10 as its base, the binary system uses 2. Furthermore, although the decimal system uses the digits 0 through 9, the binary system uses only 0 and 1, and each digit is referred to as a bit.

Almost all modern technology and computers use the binary system due to its ease of implementation in digital circuitry using logic gates. It is much simpler to design hardware that only needs to detect two states, on and off (or true/false, present/absent, etc.).

Binary/Decimal Conversion Table

How Binary Conversion Works

Each binary place value represents 2ⁿ, just as each decimal place represents 10ⁿ. Take the number 8 for example:

To convert decimal to binary:

1. Find the largest power of 2 that lies within the given number
2. Subtract that value from the given number
3. Find the largest power of 2 within the remainder found in step 2
4. Repeat until there is no remainder
5. Enter a 1 for each binary place value that was found, and a 0 for the rest

Binary Addition

Binary addition follows the same rules as addition in the decimal system except that rather than carrying a 1 over when the values added equal 10, carry over occurs when the result of addition equals 2.