2.2 Basic Logic Operation

There are only 3 basic logical operation:

1. Logical Addition or the OR function

x + y = F

The foundation of Boolean algebra and, consequently, all digital logic, rests upon three fundamental logical operations: Logical Addition (OR function), Logical Multiplication (AND function), and Logical Complementation (NOT function). The Logical Addition, or OR function, represented by the symbol '+' (as in x+y=F), yields a true output (typically '1') if at least one of its inputs is true. It functions much like the everyday use of the word "or," where having either condition met is sufficient for the outcome to be true. For instance, if 'x' is true OR 'y' is true, the result 'F' is true. Only when all inputs are false does the OR function produce a false output ('0').

2. Logical Multiplication or the AND function

xy = F

In contrast, the Logical Multiplication, or AND function, represented by juxtaposition or an implicit multiplication symbol (as in xy=F), requires all of its inputs to be true to produce a true output. Analogous to the word "and" in common language, if 'x' is true AND 'y' is true, then and only then is the result 'F' true. If even one of the inputs is false, the AND function's output will be false. This operation is crucial for situations where multiple conditions must simultaneously be met for a certain outcome.

1. Logical Complementation or the NOT function

Y’ = F

Finally, the Logical Complementation, or NOT function, denoted by a prime symbol (as in Y ′=F), is a unary operation, meaning it operates on a single input. Its role is to invert the logical state of its input. If the input 'Y' is true, its complement 'Y'' will be false, and conversely, if 'Y' is false, then 'Y'' will be true. This function is essential for creating inverse conditions and for building more complex logical structures where a signal needs to be toggled or negated. Together, these three simple yet powerful operations form the building blocks for constructing intricate digital circuits and for performing complex logical reasoning within computing systems.