How can binary arithmetic operations be reduced to Boolean algebra operations?

Binary arithmetic operations—addition, subtraction, multiplication, and division—are performed by digital computers by reducing them to fundamental Boolean algebraic operations.1

Because computers operate on a two-valued system where data is represented by binary code (0 and 1), they utilize logic gates to process information. These gates are physical implementations of Boolean operators such as AND, OR, and NOT. By connecting these gates in specific configurations, engineers can construct circuits capable of executing arithmetic functions.123

For instance, complex operations are broken down into sequences of these basic logical steps. The output of one gate serves as the input for another, allowing the system to manipulate bits to produce the correct mathematical result. This integration of formal logic and electronic circuitry is the foundational principle behind modern computing architecture.23