Acetaldehyde - Revision history

en>Drbogdan: Reverted good faith edits by 70.109.42.135: Rv possibly good faith but uncited ip edit - please discuss on the talk page - per WP:BRD, WP:CITE & related. (TW)

2015-01-10T20:07:39Z

Reverted good faith edits by 70.109.42.135: Rv possibly good faith but uncited ip edit - please discuss on the talk page - per WP:BRD, WP:CITE & related. (TW)

← Older revision		Revision as of 22:07, 10 January 2015
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en>Edgar181: Undid revision 596866737 by 2601:7:8180:495:9D83:73A6:98D6:BE5D (talk)

2014-02-24T13:35:26Z

Undid revision 596866737 by 2601:7:8180:495:9D83:73A6:98D6:BE5D (talk)

← Older revision		Revision as of 15:35, 24 February 2014
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	~~{{Distinguish2\|[[combinatory logic]],~~ a ~~topic in mathematical logic}}~~		As a trusted expert on world business developments which includes ?big data?, self-employment and the social media trend, I attempt to create only the best quality and most sound data. I'm the writer of the award winning publication, How To Market for the Freelancer and a frequent speaker for several [http://www.bbc.co.uk/search/?q=online+organisations online organisations]. I have talked about worldwide mega trends, big data and the social media trend at seminars and business gatherings around the globe.<br><br>Visit my web blog cheap vacation package deals; [http://4crv.com/4 Click To See More],

	~~In [[digital circuit]] theory~~, ~~'''combinational logic''' (sometimes also referred to as '''time~~-~~independent logic'''<ref>~~
	~~C.J. Savant, Jr.; Martin Roden; Gordon Carpenter.~~
	~~"Electronic Design: Circuits~~ and ~~Systems".~~
	~~1991.~~
	~~ISBN 0-8053-0285-9~~
	~~p. 682~~
	~~</ref>~~
	~~) is a type of [[digital logic]] which is implemented by [[Boolean circuit]]s~~, ~~where the output is a [[pure function]] of the present input only. This is in contrast~~ to ~~[[sequential logic]], in which the output depends not~~ only ~~on the present input but also on the history of~~ the ~~input. In other words, sequential logic has ''[[computer storage\|memory]]'' while combinational logic does not.~~

	~~Combinational logic is used in [[computer]] circuits to perform [[Boolean algebra (logic)\|Boolean algebra]] on input signals~~ and ~~on stored~~ data. ~~Practical computer circuits normally contain a mixture~~ of ~~combinational and sequential logic. For example~~, the part of an [[arithmetic logic unit]], or ALU, that does mathematical calculations is constructed using combinational logic. Other circuits used in computers, such as [[half adder]]s, [[full adder]]s, [[half subtractor]]s, [[Half subtractor\|full subtractor]]s, [[multiplexer]]s, [[Multiplexer\|demultiplexer]]s, [[encoder]]s and ~~[[decoder]]s are also made by using combinational logic.~~

	~~==Representation==~~
	Combinational logic is used to build circuits that produce specified outputs from certain inputs. The construction of combinational logic is generally done using one of two methods: a sum of products, or a product of sums. A sum of products can be visualized in a ~~truth table, as in this example:~~

	~~{\| class="wikitable" style="margin: 1em auto 1em auto; text-align:center;"~~
	\|-
	~~! <math>A</math> \|\| <math>B</math> \|\| <math>C</math> \|\| Result \|\|~~ [~~[logical equivalence\|Logical equivalent]]~~
	\|-
	~~\| F \|\| F \|\| F \|\| F \|\| <math>\neg A \cdot \neg B \cdot \neg C</math>~~
	\|-
	~~\| F \|\| F \|\| T \|\| F \|\| <math>\neg A \cdot \neg B \cdot C</math>~~
	\|-
	~~\| F \|\| T \|\| F \|\| F \|\| <math>\neg A \cdot B \cdot \neg C</math>~~
	\|-
	~~\| F \|\| T \|\| T \|\| F \|\| <math>\neg A \cdot B \cdot C</math>~~
	\|-
	~~\| T \|\| F \|\| F \|\| T \|\| <math>A \cdot \neg B \cdot \neg C</math>~~
	\|-
	~~\| T \|\| F \|\| T \|\| F \|\| <math>A \cdot \neg B \cdot C</math>~~
	\|-
	~~\| T \|\| T \|\| F \|\| F \|\| <math>A \cdot B \cdot \neg C</math>~~
	\|-
	~~\| T \|\| T \|\| T \|\| T \|\| <math>A \cdot B \cdot C</math>~~
	\|}

	~~Using sum of products, all logical statements which yield true results are summed, giving the result:~~

	: ~~<math>A \cdot \neg B \cdot \neg C + A \cdot B \cdot C \,<~~/~~math>~~

	~~Using [[Boolean algebra (logic)\|Boolean algebra]], the result simplifies to the following equivalent of the truth table:~~

	~~: <math>A \cdot (\neg B \cdot \neg C + B \cdot C) \,<~~/~~math>~~

	~~==Logic formula minimization==~~
	~~Minimization (simplification) of combinational logic formulas is done using the following rules:~~

	~~: <math>(A + B) \cdot (A + C) = A + (B \cdot C)<~~/~~math>~~
	~~: <math>\quad (A \cdot B) + (A \cdot C) = A \cdot (B + C)<~~/~~math>~~

	~~: <math>A + (A \cdot B) = A</math>~~
	~~: <math>\quad A \cdot (A + B) = A</math>~~

	~~: <math>A + (\lnot A \cdot B)~~ = A + ~~B</math>~~
	~~: <math>\quad A \cdot(\lnot A + B) = A \cdot B</math>~~

	~~: <math>(A + B)\cdot(\lnot A + B)=B</math>~~
	~~: <math>\quad (A \cdot B) + (\lnot A \cdot B)=B</math>~~

	~~: <math>(A \cdot B) + (\lnot A \cdot C) + (B \cdot C) = (A \cdot B) + (\lnot A \cdot C)</math>~~
	~~: <math>(A + B) \cdot (\lnot A + C) \cdot (B + C) = (A + B) \cdot (\lnot A + C)</math>~~

	~~With the use of minimization (sometimes called [[logic optimization~~]~~]), a simplified logical function or circuit may be arrived upon~~, and the ~~logic [[combinational circuit]] becomes smaller,~~ and ~~easier to analyse, use, or build.~~

	~~== Terminology ==~~

	~~Some people claim that the term "combinatorial logic" is preferred over "combinational circuit",~~
	~~although others make~~ the ~~opposite recommendation~~.
	<~~ref~~>
	~~Clive Maxfield.~~
	[http://books.google.com/books?id=kQuOKBSOz5QC&pg=PA70&dq=%22combinatorial+logic%22&hl=en&sa=X&ei=vBSdULe_LMPHqQGploDoCg&ved=0CEQQ6AEwBw#v=onepage&q=%22combinatorial%20logic%22&f=false "FPGAs: World Class Designs"].
	~~p. 70.~~
	~~2009.~~
	~~ISBN 1856176215~~
	<~~/ref~~>~~<ref>~~
	~~Cliff Cummings.~~
	[http://~~www.sunburst-design~~.com/~~papers/Technical_Text_Mistakes.pdf "Common Mistakes In Technical Texts"].~~
	~~2009.~~
	~~</ref>~~

	==See ~~also==~~
	* [[Sequential logic]]
	* [[Asynchronous logic]]
	* [[FPGA]]
	* [[Formal verification]]

	~~==References==~~
	~~{{reflist}}~~
	* Michael Predko and Myke Predko, ''Digital electronics demystified'', McGraw-Hill, 2004. ISBN 0-07-144141-7

	~~== External links ==~~
	* [http://www.ee.surrey.ac.uk/Projects/Labview/combindex.html Combinational Logic & Systems Tutorial Guide] by D. Belton, ~~R. Bigwood.~~

	~~{{DEFAULTSORT:Combinational Logic}}~~
	~~[[Category:Logic in computer science]]~~
	~~[[Category:Digital electronics]]~~

129.240.192.199 at 09:28, 3 February 2014

2014-02-03T09:28:51Z

← Older revision		Revision as of 11:28, 3 February 2014
Line 1:		Line 1:
	I'~~m Modesto~~ (30) from ~~Munchen~~, ~~Germany~~. <br>~~I'm learning Bengali literature at~~ a ~~local college~~ and ~~I'm just about~~ to ~~graduate~~.<br>~~I have a part time job in a university~~.<br><br>~~Also visit my page~~ - [http://~~frivjuego~~.~~org~~/~~profile~~/~~epschmitz~~.html ~~Fifa 15 coin generator~~]		{{Distinguish2\|[[combinatory logic]], a topic in mathematical logic}}

			In [[digital circuit]] theory, '''combinational logic''' (sometimes also referred to as '''time-independent logic'''<ref>
			C.J. Savant, Jr.; Martin Roden; Gordon Carpenter.
			"Electronic Design: Circuits and Systems".
			1991.
			ISBN 0-8053-0285-9
			p. 682
			</ref>
			) is a type of [[digital logic]] which is implemented by [[Boolean circuit]]s, where the output is a [[pure function]] of the present input only. This is in contrast to [[sequential logic]], in which the output depends not only on the present input but also on the history of the input. In other words, sequential logic has ''[[computer storage\|memory]]'' while combinational logic does not.

			Combinational logic is used in [[computer]] circuits to perform [[Boolean algebra (logic)\|Boolean algebra]] on input signals and on stored data. Practical computer circuits normally contain a mixture of combinational and sequential logic. For example, the part of an [[arithmetic logic unit]], or ALU, that does mathematical calculations is constructed using combinational logic. Other circuits used in computers, such as [[half adder]]s, [[full adder]]s, [[half subtractor]]s, [[Half subtractor\|full subtractor]]s, [[multiplexer]]s, [[Multiplexer\|demultiplexer]]s, [[encoder]]s and [[decoder]]s are also made by using combinational logic.

			==Representation==
			Combinational logic is used to build circuits that produce specified outputs from certain inputs. The construction of combinational logic is generally done using one of two methods: a sum of products, or a product of sums. A sum of products can be visualized in a truth table, as in this example:

			{\| class="wikitable" style="margin: 1em auto 1em auto; text-align:center;"
			\|-
			! <math>A</math> \|\| <math>B</math> \|\| <math>C</math> \|\| Result \|\| [[logical equivalence\|Logical equivalent]]
			\|-
			\| F \|\| F \|\| F \|\| F \|\| <math>\neg A \cdot \neg B \cdot \neg C</math>
			\|-
			\| F \|\| F \|\| T \|\| F \|\| <math>\neg A \cdot \neg B \cdot C</math>
			\|-
			\| F \|\| T \|\| F \|\| F \|\| <math>\neg A \cdot B \cdot \neg C</math>
			\|-
			\| F \|\| T \|\| T \|\| F \|\| <math>\neg A \cdot B \cdot C</math>
			\|-
			\| T \|\| F \|\| F \|\| T \|\| <math>A \cdot \neg B \cdot \neg C</math>
			\|-
			\| T \|\| F \|\| T \|\| F \|\| <math>A \cdot \neg B \cdot C</math>
			\|-
			\| T \|\| T \|\| F \|\| F \|\| <math>A \cdot B \cdot \neg C</math>
			\|-
			\| T \|\| T \|\| T \|\| T \|\| <math>A \cdot B \cdot C</math>
			\|}

			Using sum of products, all logical statements which yield true results are summed, giving the result:

			: <math>A \cdot \neg B \cdot \neg C + A \cdot B \cdot C \,</math>

			Using [[Boolean algebra (logic)\|Boolean algebra]], the result simplifies to the following equivalent of the truth table:

			: <math>A \cdot (\neg B \cdot \neg C + B \cdot C) \,</math>

			==Logic formula minimization==
			Minimization (simplification) of combinational logic formulas is done using the following rules:

			: <math>(A + B) \cdot (A + C) = A + (B \cdot C)</math>
			: <math>\quad (A \cdot B) + (A \cdot C) = A \cdot (B + C)</math>

			: <math>A + (A \cdot B) = A</math>
			: <math>\quad A \cdot (A + B) = A</math>

			: <math>A + (\lnot A \cdot B) = A + B</math>
			: <math>\quad A \cdot(\lnot A + B) = A \cdot B</math>

			: <math>(A + B)\cdot(\lnot A + B)=B</math>
			: <math>\quad (A \cdot B) + (\lnot A \cdot B)=B</math>

			: <math>(A \cdot B) + (\lnot A \cdot C) + (B \cdot C) = (A \cdot B) + (\lnot A \cdot C)</math>
			: <math>(A + B) \cdot (\lnot A + C) \cdot (B + C) = (A + B) \cdot (\lnot A + C)</math>

			With the use of minimization (sometimes called [[logic optimization]]), a simplified logical function or circuit may be arrived upon, and the logic [[combinational circuit]] becomes smaller, and easier to analyse, use, or build.

			== Terminology ==

			Some people claim that the term "combinatorial logic" is preferred over "combinational circuit",
			although others make the opposite recommendation.
			<ref>
			Clive Maxfield.
			[http://books.google.com/books?id=kQuOKBSOz5QC&pg=PA70&dq=%22combinatorial+logic%22&hl=en&sa=X&ei=vBSdULe_LMPHqQGploDoCg&ved=0CEQQ6AEwBw#v=onepage&q=%22combinatorial%20logic%22&f=false "FPGAs: World Class Designs"].
			p. 70.
			2009.
			ISBN 1856176215
			</ref><ref>
			Cliff Cummings.
			[http://www.sunburst-design.com/papers/Technical_Text_Mistakes.pdf "Common Mistakes In Technical Texts"].
			2009.
			</ref>

			==See also==
			* [[Sequential logic]]
			* [[Asynchronous logic]]
			* [[FPGA]]
			* [[Formal verification]]

			==References==
			{{reflist}}
			* Michael Predko and Myke Predko, ''Digital electronics demystified'', McGraw-Hill, 2004. ISBN 0-07-144141-7

			== External links ==
			* [http://www.ee.surrey.ac.uk/Projects/Labview/combindex.html Combinational Logic & Systems Tutorial Guide] by D. Belton, R. Bigwood.

			{{DEFAULTSORT:Combinational Logic}}
			[[Category:Logic in computer science]]
			[[Category:Digital electronics]]

en>WriterHound: /* Alcohol */ copy edit

2012-08-24T18:27:40Z

Alcohol: copy edit

New page

I'm Modesto (30) from Munchen, Germany. <br>I'm learning Bengali literature at a local college and I'm just about to graduate.<br>I have a part time job in a university.<br><br>Also visit my page - [http://frivjuego.org/profile/epschmitz.html Fifa 15 coin generator]