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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 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", 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, a form of numeral used in a unary numeral system, most useful in counting or tallying ongoing results, such as the score in a game or sport Tally sort , a computer science counting and sorting algorithm
It is thought by some to be a tally stick, as it features a series of what has been interpreted as tally marks carved in three columns running the length of the tool, though it has also been suggested that the scratches might have been to create a better grip on the handle or for some other non-mathematical reason. Others argue that the marks ...
Radix, radix point, mixed radix, exponentiation; Unary numeral system (base 1) . Tally marks – Numeral form used for counting; Binary numeral system (base 2); Negative base numeral system (base −2)