What is the binary representation of the decimal number 239?

The binary representation of the decimal number 239 is 11101111.

To convert a decimal number to binary, we use a process of dividing by 2 and tracking the remainders. Let's break down how we convert the decimal number 239 into binary.

First, divide 239 by 2. The quotient is 119 and the remainder is 1. This remainder is the least significant bit (rightmost bit) of the binary representation.

Next, divide the quotient 119 by 2. The new quotient is 59 and the remainder is 1. This remainder is the next bit in the binary representation, moving from right to left.

Continuing this process, divide 59 by 2 to get a quotient of 29 and a remainder of 1. Then, divide 29 by 2 to get a quotient of 14 and a remainder of 1.

Divide 14 by 2 to get a quotient of 7 and a remainder of 0. Then, divide 7 by 2 to get a quotient of 3 and a remainder of 1.

Finally, divide 3 by 2 to get a quotient of 1 and a remainder of 1. At this point, since the quotient is less than 2, we stop the process and the quotient itself becomes the most significant bit (leftmost bit) of the binary representation.

So, putting all the remainders together from bottom to top, the binary representation of 239 is 11101111.

This method of converting decimal to binary is known as the 'division by 2' algorithm. It's a fundamental concept in computer science, as binary representation is at the core of how computers process and store data. Understanding this process is key to understanding more complex topics in computer science, such as data structures and algorithms.