loknum

Loknum is a theoretical concept in numeration studies used to explore nonstandard numeral systems. It denotes a discrete value encoded as a finite sequence of digits, with a variable place-value scheme in which the weight assigned to each digit can change according to a predefined base sequence. This contrasts with conventional positional systems that use a fixed base for all positions.

The term loknum combines a fictional root lok, drawn from discussions of nonuniform numeration, with num, the common shorthand for number. In discussions, loknum serves as a model to examine how altering place weights affects representation, arithmetic, and encoding efficiency.

Definition and computation commonly describe a loknum as a string of digits d_k d_{k-1} ... d_0, together with a corresponding sequence of place weights w_0, w_1, ..., w_k. The value of the loknum is computed as V = sum_{i=0}^k d_i w_i. The base-rule that generates the weights defines how the weights change from one position to the next; when all w_i are equal, the system reduces to a standard fixed-base numeral system.

Properties of loknums depend on the chosen base sequence. Under suitable constraints, representations can be unique; arithmetic operations require adapted rules for carrying and normalization, reflecting the nonuniform place values.

Applications include theoretical computer science, pedagogy for illustrating numeral systems, and studies of computational models that employ variable place values.

See also: numeral system, positional notation, variable-base numeral system, nonstandard numeration.