Explain how Boolean values are represented in binary.

Boolean values are represented in binary as 1 for true and 0 for false.

In the binary number system, which is base 2, there are only two possible values a digit can have: 0 and 1. These two values are used to represent the two possible states of a Boolean value: false and true, respectively. This is a fundamental concept in computer science, as binary is the basic language of computers.

When a computer processes data, it does so by manipulating binary digits, or bits. Each bit can be either a 0 or a 1, and these bits are used to represent all types of data, including numbers, text, images, and more. However, when it comes to representing Boolean values, the process is quite straightforward. A Boolean value of true is represented as a binary 1, and a Boolean value of false is represented as a binary 0.

This binary representation of Boolean values is used in many areas of computer science. For example, in programming, Boolean values are often used to control the flow of a program. If a certain condition is true (1), then a certain block of code will be executed. If the condition is false (0), then the code will be skipped.

In digital electronics, Boolean values are used to represent the state of electronic switches, or gates. A switch that is on (allowing current to flow) is represented as a 1, and a switch that is off (not allowing current to flow) is represented as a 0. This is the basis for how computers process and store data.

In summary, Boolean values are represented in binary as 1 for true and 0 for false. This simple binary representation is a fundamental concept in computer science, and is used in many different areas, from programming to digital electronics.