Truth tables and circuit diagrams fall short in many ways including their abilities to evaluate and manipulate combinational logic. By using algebraic methods to represent logic expressions, we can apply properties and identities to improve performance.
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Tarnoff, David, "Episode 4.05 – Introduction to Boolean Algebra" (2020). Computer Organization and Design Fundamentals Series. https://dc.etsu.edu/computer-organization-design-oer/33