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{{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.
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==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]]

Latest revision as of 22:07, 10 January 2015


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For more than a decade now, Costa Rica happens to be readying themselves to be the frontmost experts in succeeding as an environmentally aware region.

As a result it has formed a wholly unique generation of eco-friendly traveler who's in tune with their effect on the globe.

There was just lately a survey carried out by probably the most notable travel web-pages on the Net that suggested the expanding interest by travellers that are in-tune with their ecological impact on the Earth.

earth

With Costa Rica taking pole position in the survey, this would unsurprisingly have a fantastic positive bearing on the already expanding Costa Rica tourism industry and a selection of others.

Interestingly the real estate sector further would favor from this new world knowledge.

Ahead of the world economic crisis hit, Costa Rica real estate was a prospering market alongside sales peaking - MSNBC would even call this sector one of the leading on the earth. Then little by little the situation hit the small Latin American nation.

And it hit really hard!

But that was the past and now...

These days with the rise in consciousness with regards to the ecosystem, so many individual traders and sizable businesses equally are seeing that the Costa Rica properties marketplace is really worth their consideration.

A major element when considering the marketing opportunities is the ability for companies to use the tag line "ecologically friendly" -- the reality is there are a smattering of hotels and resorts in Costa Rica with Green Leaf recognition.

The ideal bit is... it's conceivable here given the foundation is set as the balance of the society becomes more conscious -- with incredible Costa Rica marketing efforts by ICT (Costa Rica Tourism) and many other companies that have selected to open shop in the most ecologically friendly region on the planet!

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