In Boolean algebra, what does A + A' equal?

In Boolean algebra, the expression A + A' represents the logical OR operation between a variable A and its complement A'. The key principle at work here is that A' is the negation of A; if A is true (1), A' is false (0), and vice versa.

When evaluating A + A', we notice that regardless of the value of A, the expression will always yield a true result. If A is true (1), A' is false (0), resulting in 1 + 0 = 1. Conversely, if A is false (0), A' is true (1), resulting in 0 + 1 = 1. Thus, the outcome of A + A' is always 1, which reflects the fundamental property of a variable and its complement in Boolean algebra: they cover all possible states (true and false).

This property is foundational in digital electronics, as it establishes behaviors in logic circuits using OR gates, where the output reflects the presence of A or its negation. Understanding this relationship between a variable and its complement is crucial for simplifying expressions and designing circuits.