ANDreduction

andReduction is a reduction operation that computes the logical AND across all elements of a collection or vector. It yields a single result that reflects whether every input element meets a specified condition (typically being true or equal to 1). In boolean terms, the and-reduction computes the conjunction of all inputs: the output is true if and only if every input is true.

In digital design and hardware description languages, the reduction operator commonly called the AND reduction collapses a multi-bit vector into one bit. For a bit vector [b_n-1, ..., b_0], the reduction value is b_n-1 ∧ ... ∧ b_0. In Verilog, this is written as an expression like result = &vector, where the ampersand denotes the reduction across the entire vector. This is distinct from a bitwise AND, which operates on corresponding positions of two vectors and yields a vector.

In software, AND-reduction can be implemented via folding, reducing, or using built-in helpers. For example, many languages provide a reduce function with the logical AND operator, or a function like all() that returns true only if every element is truthy. This mirrors the same logical intent as the hardware reduction: determine if every input satisfies the condition.

Applications include condition checking across multiple flags, validation of multiple prerequisites, and aggregation of status signals in pipelines or control logic. Variants exist for non-boolean data, where the operation is applied bitwise across all elements, often with attention to data width and representation. The concept is closely related to universal quantification in logic and to the broader family of reduction operations, which also includes OR and XOR reductions.