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{{Unreferenced|date=December 2009}}
This is a preview for the new '''MathML rendering mode''' (with SVG fallback), which is availble in production for registered users.


In electronics, a '''carry-select adder''' is a particular way to implement an [[adder (electronics)|adder]], which is a logic element that computes the <math>(n+1)</math>-bit sum of two <math>n</math>-bit numbers. The carry-select adder is simple but rather fast, having a gate level depth of <math>O(\sqrt n)</math>.
If you would like use the '''MathML''' rendering mode, you need a wikipedia user account that can be registered here [[https://en.wikipedia.org/wiki/Special:UserLogin/signup]]
* Only registered users will be able to execute this rendering mode.
* Note: you need not enter a email address (nor any other private information). Please do not use a password that you use elsewhere.


The carry-select adder generally consists of two [[Adder (electronics)#Multiple-bit adders|ripple carry adder]]s and a [[multiplexer]]. Adding two n-bit numbers with a carry-select adder is done with two adders (therefore two ripple carry adders) in order to perform the calculation twice, one time with the assumption of the carry being zero and the other assuming one. After the two results are calculated, the correct sum, as well as the correct carry, is then selected with the multiplexer once the correct carry is known.
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The number of bits in each carry select block can be uniform, or variable.  In the uniform case, the optimal delay occurs for a block size of <math>\lfloor \sqrt n \rfloor</math>.  When variable, the block size should have a delay, from addition inputs A and B to the carry out, equal to that of the multiplexer chain leading into it, so that the carry out is calculated just in time. The <math>O(\sqrt n)</math> delay is derived from uniform sizing, where the ideal number of full-adder elements per block is equal to the square root of the number of bits being added, since that will yield an equal number of MUX delays.
'''MathML'''
:<math forcemathmode="mathml">E=mc^2</math>


==Basic building block==
<!--'''PNG'''  (currently default in production)
:<math forcemathmode="png">E=mc^2</math>


[[File:Carry-select-adder-detailed-block.png|300px]]
'''source'''
:<math forcemathmode="source">E=mc^2</math> -->


Above is the basic building block of a carry-select adder, where the block size is 4. Two 4-bit ripple carry adders are multiplexed together, where the resulting carry and sum bits are selected by the carry-in. Since one ripple carry adder assumes a carry-in of 0, and the other assumes a carry-in of 1, selecting which adder had the correct assumption via the actual carry-in yields the desired result.
<span style="color: red">Follow this [https://en.wikipedia.org/wiki/Special:Preferences#mw-prefsection-rendering link] to change your Math rendering settings.</span> You can also add a [https://en.wikipedia.org/wiki/Special:Preferences#mw-prefsection-rendering-skin Custom CSS] to force the MathML/SVG rendering or select different font families. See [https://www.mediawiki.org/wiki/Extension:Math#CSS_for_the_MathML_with_SVG_fallback_mode these examples].


==Uniform-sized adder==
==Demos==


[[File:Carry-select-adder-fixed-size.png|800px]]
Here are some [https://commons.wikimedia.org/w/index.php?title=Special:ListFiles/Frederic.wang demos]:


A 16-bit carry-select adder with a uniform block size of 4 can be created with three of these blocks and a 4-bit ripple carry adder. Since carry-in is known at the beginning of computation, a carry select block is not needed for the first four bits. The delay of this adder will be four full adder delays, plus three MUX delays


==Variable-sized adder==
* accessibility:
** Safari + VoiceOver: [https://commons.wikimedia.org/wiki/File:VoiceOver-Mac-Safari.ogv video only], [[File:Voiceover-mathml-example-1.wav|thumb|Voiceover-mathml-example-1]], [[File:Voiceover-mathml-example-2.wav|thumb|Voiceover-mathml-example-2]], [[File:Voiceover-mathml-example-3.wav|thumb|Voiceover-mathml-example-3]], [[File:Voiceover-mathml-example-4.wav|thumb|Voiceover-mathml-example-4]], [[File:Voiceover-mathml-example-5.wav|thumb|Voiceover-mathml-example-5]], [[File:Voiceover-mathml-example-6.wav|thumb|Voiceover-mathml-example-6]], [[File:Voiceover-mathml-example-7.wav|thumb|Voiceover-mathml-example-7]]
** [https://commons.wikimedia.org/wiki/File:MathPlayer-Audio-Windows7-InternetExplorer.ogg Internet Explorer + MathPlayer (audio)]
** [https://commons.wikimedia.org/wiki/File:MathPlayer-SynchronizedHighlighting-WIndows7-InternetExplorer.png Internet Explorer + MathPlayer (synchronized highlighting)]
** [https://commons.wikimedia.org/wiki/File:MathPlayer-Braille-Windows7-InternetExplorer.png Internet Explorer + MathPlayer (braille)]
** NVDA+MathPlayer: [[File:Nvda-mathml-example-1.wav|thumb|Nvda-mathml-example-1]], [[File:Nvda-mathml-example-2.wav|thumb|Nvda-mathml-example-2]], [[File:Nvda-mathml-example-3.wav|thumb|Nvda-mathml-example-3]], [[File:Nvda-mathml-example-4.wav|thumb|Nvda-mathml-example-4]], [[File:Nvda-mathml-example-5.wav|thumb|Nvda-mathml-example-5]], [[File:Nvda-mathml-example-6.wav|thumb|Nvda-mathml-example-6]], [[File:Nvda-mathml-example-7.wav|thumb|Nvda-mathml-example-7]].
** Orca: There is ongoing work, but no support at all at the moment [[File:Orca-mathml-example-1.wav|thumb|Orca-mathml-example-1]], [[File:Orca-mathml-example-2.wav|thumb|Orca-mathml-example-2]], [[File:Orca-mathml-example-3.wav|thumb|Orca-mathml-example-3]], [[File:Orca-mathml-example-4.wav|thumb|Orca-mathml-example-4]], [[File:Orca-mathml-example-5.wav|thumb|Orca-mathml-example-5]], [[File:Orca-mathml-example-6.wav|thumb|Orca-mathml-example-6]], [[File:Orca-mathml-example-7.wav|thumb|Orca-mathml-example-7]].
** From our testing, ChromeVox and JAWS are not able to read the formulas generated by the MathML mode.


[[File:Carry-select-adder-variable-size.png|800px]]
==Test pages ==


A 16-bit carry-select adder with variable size can be similarly created. Here we show an adder with block sizes of 2-2-3-4-5. This break-up is ideal when the full-adder delay is equal to the MUX delay, which is unlikely. The total delay is two full adder delays, and four mux delays.We try to make the delay through the two carry chains and the delay of the previous stage carry equal.
To test the '''MathML''', '''PNG''', and '''source''' rendering modes, please go to one of the following test pages:
*[[Displaystyle]]
*[[MathAxisAlignment]]
*[[Styling]]
*[[Linebreaking]]
*[[Unique Ids]]
*[[Help:Formula]]


==Combining with other adder structures==
*[[Inputtypes|Inputtypes (private Wikis only)]]
 
*[[Url2Image|Url2Image (private Wikis only)]]
This adder design can be complemented with a [[carry-lookahead adder]] structure to generate the MUX inputs, thus gaining even greater performance as a parallel prefix adder while potentially reducing area. An example is shown in the [[Kogge–Stone adder]] article.
==Bug reporting==
 
If you find any bugs, please report them at [https://bugzilla.wikimedia.org/enter_bug.cgi?product=MediaWiki%20extensions&component=Math&version=master&short_desc=Math-preview%20rendering%20problem Bugzilla], or write an email to math_bugs (at) ckurs (dot) de .
{{DEFAULTSORT:Carry-select adder}}
[[Category:Adders]]
 
[[de:Carry-Select-Addierer]]

Latest revision as of 22:52, 15 September 2019

This is a preview for the new MathML rendering mode (with SVG fallback), which is availble in production for registered users.

If you would like use the MathML rendering mode, you need a wikipedia user account that can be registered here [[1]]

  • Only registered users will be able to execute this rendering mode.
  • Note: you need not enter a email address (nor any other private information). Please do not use a password that you use elsewhere.

Registered users will be able to choose between the following three rendering modes:

MathML

E=mc2


Follow this link to change your Math rendering settings. You can also add a Custom CSS to force the MathML/SVG rendering or select different font families. See these examples.

Demos

Here are some demos:


Test pages

To test the MathML, PNG, and source rendering modes, please go to one of the following test pages:

Bug reporting

If you find any bugs, please report them at Bugzilla, or write an email to math_bugs (at) ckurs (dot) de .

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