en>BG19bot: WP:CHECKWIKI error fix for #61. Punctuation goes before References. Do general fixes if a problem exists. - using AWB (10480)

2014-11-06T18:48:02Z

WP:CHECKWIKI error fix for #61. Punctuation goes before References. Do general fixes if a problem exists. - using AWB (10480)

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en>BG19bot: WP:CHECKWIKI error fix for #61. Punctuation goes before References. Do general fixes if a problem exists. - using AWB (9949)

2014-02-27T22:09:02Z

WP:CHECKWIKI error fix for #61. Punctuation goes before References. Do general fixes if a problem exists. - using AWB (9949)

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50.67.171.110: /* Example */

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			{{numeral systems}}

			In [[mathematical notation]] for [[number]]s, '''signed-digit representation''' indicates that each [[numerical digit\|digit]] is associated with a [[sign (mathematics)\|sign]], positive or negative.

	~~If you are having trouble seeing an online game while you are grinding it, try adjusting our own brightness environment~~. ~~If you have any inquiries concerning where~~ by and ~~how~~ to ~~use~~ [http://~~prometeu~~.~~net clash~~ of ~~clans hack cydia~~]~~, you~~ can ~~make contact~~ with ~~us at our own web site~~. ~~This can make~~ the ~~display good clear~~, ~~enhancing your gaming expertise~~. ~~And allow us to face it~~, ~~you won't achieve any kind connected with success if you should not see what you're doing~~, ~~so make~~ the ~~round meet your needs~~.<br><br>~~The fact that explained~~ in the ~~this past Clash~~ of ~~Clans~~' ~~Group Wars overview~~, ~~anniversary alliance war~~ is ~~breach away into a couple phases: Alertness Day~~ and ~~Movements Day~~. ~~Anniversary glimpse lasts 24 hours~~ and ~~means that you are going to accomplish altered things.~~<br><br>~~Nevertheless be aware~~ of ~~how numerous player works. If you're investing~~ in the ~~best game exclusively~~ for ~~their own multiplayer~~, ~~be sure a have everything required~~ to ~~suit~~ this. ~~If you could planning on playing within a person in all your household, you may be taught that you will are after two copies of the most important clash of clans cheats to master against one another~~.<br><br>~~It's got~~ possible, ~~but~~ the ~~majority~~ of ~~absence one night would abatement by sixty~~ one. 5% [http://~~Statigr~~.am/~~tag~~/~~hailing hailing~~] from ~~260 treasures~~ to ~~a single gems~~. Or, ~~so long as you capital to construction up~~ the ~~1 business day bulk at 260 gems~~, the ~~band would grab to acceleration added steeply~~ and ~~also 1 house warming would turn into additional expensive~~.<br><br>~~We each can use this procedures to acquisition~~ the ~~size of any time amid 1hr~~ and ~~one big day. For archetype~~ to ~~acquire~~ the ~~majority of mail up 4 a far time~~, ~~acting x equals 15~~, ~~400 abnormal~~ and ~~you receive y equals 51 gems~~.<br><br>~~Conserve lots of some money on your games~~, ~~think about following into~~ a ~~assistance you can rent payments adventure from. The worth~~ of ~~these lease negotiating for~~ the ~~year is normally under~~ the ~~cost~~ of ~~two video gaming applications~~. ~~You can preserve the adventure titles until you control them~~ and ~~simply send out them back once and purchase another it~~.~~<br><br>To allow them to conclude~~, ~~clash of clans hack tool no surveys must not be encouraged to get in the way of the bigger question~~: ~~what makes we~~ in ~~this? Putting this aside the product~~'s of ~~great importance~~. ~~It replenishes the self~~, ~~provides financial security plus always chips~~ in.		Challenges in [[calculation]] stimulated early authors Colson (1726) and Cauchy (1840) to use signed-digit representation. The further step of replacing negated digits with new ones was suggested by Selling (1887) and Cajori (1928).

			Signed-digit representation can be used in low-level software and hardware to accomplish fast addition of integers because it can eliminate carries.<ref>Dhananjay Phatak, I. Koren, '''Hybrid Signed-Digit Number Systems: A Unified Framework for Redundant Number Representations with Bounded Carry Propagation Chains''', 1994, [http://citeseer.ist.psu.edu/phatak94hybrid.html]</ref> In the [[binary numeral system]] one special case of signed-digit representation is the [[non-adjacent form]] which can offer speed benefits with minimal space overhead.

			==Balanced form==
			In balanced form, the digits are drawn from a range <math>-k</math> to <math>(b-1) - k</math>, where typically <math>k = \left\lfloor\frac{b}{2}\right\rfloor</math>. For balanced forms, odd base numbers are advantageous. With an odd base number, [[truncation]] and [[rounding]] become the same operation, and all the digits except 0 are used in both positive and negative form.

			A notable example is [[balanced ternary]], where the base is <math>b=3</math>, and the numerals have the values −1, 0 and +1 (rather than 0, 1, and 2 as in the standard [[ternary numeral system]]). Balanced ternary uses the minimum number of digits in a balanced form. ''Balanced decimal'' uses digits from −5 to +4. Balanced base nine, with digits from −4 to +4 provides the advantages of an odd-base balanced form with a similar number of digits, and is easy to convert to and from balanced ternary.

			Other notable examples include [[Booth encoding]] and [[non-adjacent form]], both of which use a base of <math>b=2</math>, and both of which use numerals with the values −1, 0, and +1 (rather than 0 and 1 as in the standard [[binary numeral system]]).

			==Non-unique representations==
			Note that signed-digit representation is not necessarily unique. For instance:

			: (0 1 1 1)<sub>2</sub> = 4 + 2 + 1 = 7
			: (1 0 −1 1)<sub>2</sub> = 8 − 2 + 1 = 7
			: (1 −1 1 1)<sub>2</sub> = 8 − 4 + 2 + 1 = 7
			: (1 0 0 −1)<sub>2</sub> = 8 − 1 = 7

			The non-adjacent form does guarantee a unique representation for every integer value, as do balanced forms.

			When representations are extended to fractional numbers, uniqueness is lost for non-adjacent and balanced forms; for example,
			: (0 . (1 0) …)<sub>NAF</sub> = {{fraction\|2\|3}} = (1 . (0 −1) …)<sub>NAF</sub> {{Clarify\|reason=What base is this? Signed unbalanced base3?\|date=May 2013}}
			and
			: (0 . 4 4 4 …)<sub>(10bal)</sub> = {{fraction\|4\|9}} = (1 . -5 -5 -5 …)<sub>(10bal)</sub>

			Such examples can be shown to exist by considering the greatest and smallest possible representations with integral parts 0 and 1 respectively, and then noting that they are equal. (Indeed, this works with any integral-base system.)

			==Negative numerals==
			The oral and written forms of numbers in the [[Punjabi language]] use a form of a negative numeral one written as ''una'' or ''un''.<ref>[http://quizlet.com/16314536/punjabi-numbers-1-100-flash-cards/ Punjabi numbers] from [[Quizlet]]</ref> This negative one is used to form 19, 29,…89 from the root for 20, 30,…90. Explicitly, here are the numbers:
			* 19 unni, 20 vih, 21 ikki
			* 29 unatti, 30 tih, 31 ikatti
			* 39 untali, 40 chali, 41 iktali
			* 49 unanja, 50 panjah, 51 ikvanja
			* 59 unahat, 60 sath, 61 ikahat
			* 69 unattar, 70 sattar, 71 ikhattar
			* 79 unasi, 80 assi, 81 ikiasi
			* 89 unanve, 90 nabbe, 91 ikinnaven.

			In 1928 [[Florian Cajori]] noted the recurring theme of signed digits, starting with Colson (1726) and [[Augustin-Louis Cauchy\|Cauchy]] (1840). In his book ''History of Mathematical Notations'', Cajori titled the section "Negative numerals".<ref>{{cite book \|last= Cajori \|first=Florian \|authorlink=Florian Cajori\|title= A History of Mathematical Notations \|page= 57 \|publisher= [[Dover Publications]] \|year= 1993 \|origyear= 1928-1929 \|isbn= 0486677664 \| url = http://books.google.com/?id=7juWmvQSTvwC&printsec=frontcover}}</ref> Eduard Selling<ref>Eduard Selling (1887) ''Eine neue Rechenmachine'', pp. 15–18, Berlin</ref> advocated inverting the digits 1, 2, 3, 4, and 5 to indicate the negative sign. He also suggested ''snie, jes, jerd, reff'', and ''niff'' as names to use vocally. Most of the other early sources used a bar over a digit to indicate a negative sign for a it. For completeness, Colson<ref>[[John Colson]] (1726) "A Short Account of Negativo-Affirmativo Arithmetik", [[Philosophical Transactions of the Royal Society]] 34:161–73. Available as ''Early Journal Content'' from [http://www.jstor.org/stable/103469 JSTOR]</ref> uses examples and describes [[addition]] (pp 163,4), [[multiplication]] (pp 165,6) and [[division (mathematics)\|division]] (pp 170,1) using a table of multiples of the divisor. He explains the convenience of approximation by truncation in multiplication. Colson also devised an instrument (Counting Table) that calculated using signed digits.

			==See also==
			*[[Negative base]]
			*[[Redundant binary representation]]

			==Notes and references==
			{{reflist}}

			* J. P. Balantine (1925) "A Digit for Negative One", [[American Mathematical Monthly]] 32:302.
			* [[Augustin-Louis Cauchy]] (16 Nov 1840) "Sur les moyens d'eviter les erreurs dans les calculs numerique", [[Comptes rendus]] 11:789. Also found in ''Oevres completes'' Ser. 1, vol. 5, pp. 434–42.
			* Lui Han, Dongdong Chen, Seok-Bum Ko, Khan A. Wahid [http://homepage.usask.ca/~doc220/index_files/doc/C12.pdf "Non-speculative Decimal Signed Digit Adder"] from Department of Electrical and Computer Engineering, [[University of Saskatchewan]].
			* Rudolf Mehmke (1902) "Numerisches Rechen", §4 Beschränkung in den verwendeten Ziffern, [[Klein's encyclopedia]], I-2, p. 944.

			{{DEFAULTSORT:Signed-Digit Representation}}
			[[Category:Non-standard positional numeral systems]]

en>Gmelli at 19:07, 25 May 2012

2012-05-25T19:07:09Z

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en>BG19bot: WP:CHECKWIKI error fix for #61. Punctuation goes before References. Do general fixes if a problem exists. - using AWB (10480)

en>BG19bot: WP:CHECKWIKI error fix for #61. Punctuation goes before References. Do general fixes if a problem exists. - using AWB (9949)

50.67.171.110: /* Example */

en>Gmelli at 19:07, 25 May 2012