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Decimal to Binary Converter

Decimal to Binary Converter

A Decimal to Binary Converter tool is a utility that translates numbers from the decimal (base-10) numerical system to the binary (base-2) numerical system. The decimal system is the standard system for denoting integer and non-integer numbers. It is based on ten distinct digits, from 0 to 9. In contrast, the binary system is used extensively in computing and digital electronics and uses only two digits, 0 and 1, to represent numbers.

The conversion process from decimal to binary involves dividing the decimal number by 2 and recording the remainder as a binary digit (bit). This division process is repeated with the quotient obtained from the previous division until the quotient becomes 0. The binary number is then formed by concatenating all the remainders in reverse order, starting from the last remainder obtained to the first.

For example, to convert the decimal number 13 to binary:

  • 13 divided by 2 gives a quotient of 6 and a remainder of 1 (first binary digit).
  • 6 divided by 2 gives a quotient of 3 and a remainder of 0 (second binary digit).
  • 3 divided by 2 gives a quotient of 1 and a remainder of 1 (third binary digit).
  • 1 divided by 2 gives a quotient of 0 and a remainder of 1 (fourth binary digit).

Therefore, the binary representation of the decimal number 13 is 1101.