How do you convert a decimal number to its binary equivalent?

To convert a decimal number to binary, repeatedly divide the number by 2 and record the remainder until the quotient is 0.

In more detail, the process of converting a decimal number to binary involves a series of divisions by 2, where the remainder of each division becomes a binary digit (bit) in the binary equivalent. This process is also known as 'double dabble'.

Let's take an example. Suppose we want to convert the decimal number 13 to binary. Here's how we would do it:

1. Divide 13 by 2. The quotient is 6 and the remainder is 1. So, the least significant bit (rightmost bit) of the binary equivalent is 1.
2. Divide the quotient from the previous step (6) by 2. The new quotient is 3 and the remainder is 0. So, the next bit is 0.
3. Repeat the process with the new quotient (3). The quotient is 1 and the remainder is 1. So, the next bit is 1.
4. Finally, divide the last quotient (1) by 2. The quotient is 0 and the remainder is 1. So, the most significant bit (leftmost bit) is 1.

So, the binary equivalent of the decimal number 13 is 1101.

It's important to note that the binary digits are obtained in reverse order, from least significant to most significant. Therefore, after obtaining all the bits, you should reverse the sequence to get the correct binary equivalent.

This method works for any positive integer. For decimal fractions, a similar but slightly more complex process is used, involving repeated multiplications by 2 instead of divisions. For negative integers, a method called 'two's complement' is used, which involves flipping all the bits of the binary equivalent of the absolute value of the number and then adding 1.

Remember, understanding binary is fundamental to computer science because all digital data is ultimately represented as binary information, with 0s and 1s representing off and on states in digital circuits.