How is a decimal number converted to binary?

The process of converting a decimal number to binary is effectively done by sequentially dividing the decimal number by 2 and recording the remainders. This technique works because the binary system is base 2, meaning each digit in a binary number represents a power of 2.

Starting with the decimal number, you divide it by 2. The quotient is then used for the next division, and the process continues until the quotient reaches zero. During each division, the remainder indicates how much of the next power of 2 is included in the binary representation. The binary number is formed by taking the remainders in reverse order—this gives you the final binary sequence that corresponds to the initial decimal number.

For example, if converting the decimal number 10 to binary involves dividing 10 by 2, which gives a quotient of 5 and a remainder of 0. Then dividing 5 by 2 gives a quotient of 2 and a remainder of 1, and dividing 2 by 2 gives a quotient of 1 and a remainder of 0, finally dividing 1 by 2 gives a quotient of 0 and a remainder of 1. Reading the remainders in reverse order results in 1010,