numbrik

Numbrik is a fictional numerical representation framework devised to explore alternative numeral systems and their arithmetic properties. The term blends 'numeric' and 'brick', signaling a modular, block-based approach to encoding integers as sequences of digits drawn from a finite alphabet. In Numbrik, numbers are represented as finite sequences (d_k ... d_0) of digits, and arithmetic is defined by a set of local rules that operate digitwise with carry propagation depending on a chosen base-like parameter b and a digit interaction table.

Unlike traditional positional systems, Numbrik emphasizes composability of blocks: a number can be formed by concatenating smaller Numbrik blocks, with the overall value determined by a formal evaluation rule that respects block boundaries.

Digital rules: addition and subtraction proceed digitwise with a carry or borrow rule defined by a small, fixed table. Multiplication can be defined via convolution of digit sequences with carry rules. The choice of digit set and base determines the density and efficiency of representation; some variants use balanced digits to minimize carry propagation.

Applications: Numbrik is primarily a didactic device in textbooks and puzzle collections to illustrate how changing base, digit sets, or carry rules affects arithmetic complexity. It also serves as a heuristic tool for teaching modular arithmetic, encoding schemes, and error-detecting codes in an abstract setting.

Notes: As a fictional construct, Numbrik has no standard implementation outside educational contexts. Variants exist in problem sets or programming challenges that experiment with different rule tables.

See also: numeral system, base-n numeral system, positional numeral system, modular arithmetic, digit set, carry.