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Tally marks, also called hash marks, are a form of numeral used for counting. They can be thought of as a unary numeral system . They are most useful in counting or tallying ongoing results, such as the score in a game or sport, as no intermediate results need to be erased or discarded.
Possible tally marks made by carving notches in wood, bone, and stone appear in the archaeological record at least forty thousand years ago. [9] [10] These tally marks may have been used for counting time, such as numbers of days or lunar cycles, or for keeping records of quantities, such as numbers of animals or other valuable commodities.
The single tally stick was an elongated piece of bone, ivory, wood, or stone which is marked with a system of notches (see: Tally marks). The single tally stick serves predominantly mnemonic purposes. Related to the single tally concept are messenger sticks (used by, e.g., Inuit tribes), the knotted cords, khipus or quipus, as used by the Inca.
Tally marks", Recommendations to UTC #146 January 2016 on Script Proposals L2/16-065 Lunde, Ken; Miura, Daisuke (2016-03-14), Proposal to encode two Western-style tally marks
Tally marks represent one such system still in common use. The unary system is only useful for small numbers, although it plays an important role in theoretical computer science . Elias gamma coding , which is commonly used in data compression , expresses arbitrary-sized numbers by using unary to indicate the length of a binary numeral.
Tally marks, Counting. Unary numbering is used as part of some data compression algorithms such as Golomb coding. It also forms the basis for the Peano axioms for formalizing arithmetic within mathematical logic. A form of unary notation called Church encoding is used to represent numbers within lambda calculus.
Tally marks – Numeral form used for counting; Binary numeral system (base 2) Negative base numeral system (base −2) Ternary numeral system numeral system (base 3) Balanced ternary numeral system (base 3) Negative base numeral system (base −3) Quaternary numeral system (base 4) Quater-imaginary base (base 2 √ −1) Quinary numeral system ...
Written mathematics began with numbers expressed as tally marks, with each tally representing a single unit. Numerical symbols consisted probably of strokes or notches cut in wood or stone, which were intelligible across cultures. For example, one notch in a bone represented one animal, person, or object.