Boolean algebra is a mathematical structure that deals with variables that can take only two values: true or false, represented as 1 or 0, respectively. It is named after the mathematician George Boole, who first developed this algebraic system in the mid-19th century. Boolean algebra is widely used in various fields, including computer science and digital electronics, due to its ability to represent and manipulate logical statements and operations.

1. For designing of digital computers:
Boolean algebra is extensively used in the design and analysis of digital circuits and systems, including computer architecture and digital logic design. Digital computers are based on binary logic, where information is represented using bits, which can be either 0 or 1. Boolean algebra provides a formalism to express and manipulate logic gates, such as AND, OR, and NOT gates, which are the building blocks of digital circuits. By using Boolean algebra, designers can derive logical expressions and truth tables that describe the behavior of complex digital systems.

2. In building logic symbols:
Logic symbols are graphical representations of logical operations and relationships between variables. Boolean algebra provides a foundation for creating these symbols and defining their behavior. For example, AND and OR gates are represented by specific symbols in circuit diagrams, which are derived from Boolean algebra expressions. Using logic symbols, complex digital systems can be represented visually, making it easier for engineers to understand and analyze their behavior.

3. Circuit theory:
Boolean algebra is closely related to circuit theory, which deals with the analysis and design of electrical circuits. By using Boolean algebra, circuit theorists can express circuit equations and solve them to determine the behavior of electrical systems. Boolean algebra allows for the simplification of complex circuit equations, enabling engineers to optimize circuit designs for efficiency and performance.

4. Building algebraic functions:
Boolean algebra can be used to build algebraic functions that operate on binary variables. These functions can be used for various purposes, such as data manipulation, signal processing, and control systems. Algebraic functions built using Boolean algebra can be expressed as logical expressions and implemented in digital systems using logic gates.

In conclusion, Boolean algebra is a fundamental tool for designing digital computers, building logic symbols, analyzing electrical circuits, and constructing algebraic functions. Its ability to represent and manipulate logical statements and operations makes it an essential concept in the field of computer science and digital electronics.