Sign-value notation: Difference between revisions

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{{Short description|Number representation system}}

{{about|a class of numeral signs|the sociological/economic concept of sign value|Sign value|a representation of signed numbers in computers|Sign-magnitude}}

{{Numeral systems|expand=Sign-value notation}}

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== Additive notation ==

{{redirect|Additive notation|the convention for abelian groups|Abelian group#Notation}}

[[File:Egipat2.gif|thumb|upright=1.2|Additive notation in [[Egyptian numerals]]]]

'''Additive notation'''<!--boldface per [[WP:R#PLA]]--> represents numbers by a series of numerals that added together equal the value of the number represented, much as [[tally marks]] are added together to represent a larger number. To represent multiples of the sign value, the same sign is simply repeated. In Roman numerals, for example, {{rn|X}} means ten and {{rn|L}} means fifty., Henceso {{rn|LXXX}} means eighty (50&nbsp;+&nbsp;10&nbsp;+&nbsp;10&nbsp;+&nbsp;10).

Although signs may be written in a conventional order the value of each sign does not depend on its place in the sequence, and changing the order does not affect the total value of the sequence in an additive system. Frequently used large numbers are often expressed using unique symbols to avoid excessive repetition. [[Aztec numerals]], for example, use a [[Tally marks|tally]] of dots for numbers less than twenty alongside unique symbols for powers of 20twenty, including 400 and 8,000.{{sfnp|Daniels|Bright|1996|p=796}}

== Subtractive notation ==

{{see also|Roman numerals#Subtractive notation}}

'''Subtractive notation'''<!--boldface per [[WP:R#PLA]]--> represents numbers by a series of numerals in which signs representing smaller values are typically subtracted from those representing larger values to equal the number represented. In Roman numerals, for example, {{rn|I}} means one and {{rn|X}} means ten. Hence {{rn|IX}} means nine (10&nbsp;−&nbsp;1). The consistent use of the subtractive system with Roman numerals was not standardised until after the widespread adoption of the [[printing press]] in Europe.{{sfnp|Daniels|Bright|1996|p=796}}

'''Subtractive notation'''<!--boldface per [[WP:R#PLA]]--> represents numbers by a series of numerals in which signs representing smaller values are typically subtracted from those representing larger values to equal the value of the number represented. In Roman numerals, for example, {{rn|I}} means one and {{rn|X}} means ten., Henceso {{rn|IX}} means nine (10&nbsp;−&nbsp;1). The consistent use of the subtractive system with Roman numerals was not standardised until after the widespread adoption of the [[printing press]] in Europe.{{sfnp|Daniels|Bright|1996|p=796}}

== History ==

* [[{{further|History of ancient numeral systems]]}}

Sign-value notation was the ancient way of writing numbers and only gradually evolved into place-value notation, also known as [[positional notation]]. Sign-value notations have been used across the world by a variety of cultures throughout history.

=== Mesopotamia ===

When ancient people wanted to write "two sheep" in clay, they could inscribe in clay a picture of two sheep.; Buthowever, this would be impractical when they wanted to write "twenty sheep". In [[Mesopotamia]] they used small [[Accounting token|clay token]]s to represent a number of a specific commodity, and strung the tokens like beads on a string, which were used for accounting. There was a token for one sheep and a token for ten sheep, and a different token for ten goats, etc.

To ensure that nobody could alter the number and type of tokens, they invented the [[Bulla (seal)|bulla]]; a clay envelope shaped like a hollow ball into which the tokens on a string were placed and then baked. If anybody contested the number, they could break open the clay envelope and do a recount. To avoid unnecessary damage to the record, they pressed archaic number signs on the outside of the envelope before it was baked, each sign similar in shape to the tokens they represented. Since there was seldom any need to break open the envelope, the signs on the outside became the first written language for writing numbers in clay, using sign-value notation.{{sfnp|Daniels|Bright|1996|p=796–797}}

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== See also ==

* [[History of ancient numeral systems]]

* [[Place-value notation]]

* [[Location arithmetic]], a base 2 sign-value notation invented by J. Napier in 1617

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== External links ==

* [https://web.archive.org/web/20070104051643/http://netzreport.googlepages.com/online_converter_for_dec_roman.html Online Converter] for Decimal/Roman Numerals ([[JavaScript]], [[GPL]])

[[Category:Numeral systems]]

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