Entropy estimation - Revision history

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	~~{{No footnotes\|date=April 2009}}[[File:AOI22Symbol.svg\|thumb\|250px\|right\|2-2 AOI Symbol]]~~
	~~[[File:AOI21Symbol.svg\|thumb\|250px\|right\|2-1 AOI Symbol]]~~

	'''AND-OR-Invert''' (AOI) logic and AOI gates are two-level compound (or complex) logic functions constructed from the combination of one or more [[AND gate]]s followed by a [[NOR gate]]. Construction of AOI cells is particularly efficient using [[CMOS]] technology where the total number of transistor gates can be compared to the same construction using [[NAND logic]] or [[NOR logic]]. The complement of AOI Logic is [[OR-AND-Invert]] (OAI) logic where the OR gates precede an AND gate.

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	~~AOI gates perform one~~ or ~~more [[logical~~ and~~\|AND]] operations followed by an [[logical~~ or~~\|OR]] operation~~ and ~~then an inversion~~. ~~For example~~, a ~~2-2 AOI gate~~ can be ~~represented by the [[Boolean algebra (logic)\|boolean equation]] and [[truth table]]:~~

	<~~math~~>~~F=\overline{(A \wedge B) \vee (C \wedge D)}~~<~~/math~~>

	~~{\| class=~~"~~wikitable~~"
	~~\|- bgcolor="#ddeeff" align="center"~~
	~~\|colspan=5\|2-2 AOI~~
	~~\|- bgcolor="#ddeeff" align="center"~~
	~~\|colspan=4\|'''INPUT~~'''<br>~~A   B   C   D \|\| '''OUTPUT'''~~<br> F
	~~\|- bgcolor="#ddffdd" align="center"~~
	~~\|0 \|\| X \|\| X \|\| 0 \|\| 1~~
	~~\|- bgcolor="#ddffdd" align="center"~~
	~~\|X \|\| 0 \|\| X \|\| 0 \|\| 1~~
	~~\|- bgcolor="#ddffdd" align="center"~~
	~~\|0 \|\| X \|\| 0 \|\| X \|\| 1~~
	~~\|- bgcolor="#ddffdd" align="center"~~
	~~\|X \|\| 0 \|\| 0 \|\| X \|\| 1~~
	~~\|- bgcolor="#ddffdd" align="center"~~
	~~\|1 \|\| 1 \|\| X \|\| X \|\| 0~~
	~~\|- bgcolor="#ddffdd" align="center"~~
	~~\|X \|\| X \|\| 1 \|\| 1 \|\| 0~~
	\|}

	~~A 2-1 AOI gate~~ can ~~be represented by following~~ the ~~boolean equation~~ and ~~truth table:~~

	<~~math~~>~~F=\overline{ A \vee~~ (~~B \wedge C~~)}<~~/math~~>

	~~{\| class="wikitable"~~
	~~\|- bgcolor="#ddeeff" align="center"~~
	~~\|colspan=4\|2-1 AOI~~
	~~\|- bgcolor="#ddeeff" align="center"~~
	~~\|colspan=3\|'''INPUT'''~~<br>~~A   B   C \|\| '''OUTPUT'''~~<br> F
	~~\|- bgcolor="#ddffdd" align="center"~~
	~~\|0 \|\| 0 \|\| 0 \|\| 1~~
	~~\|- bgcolor="#ddffdd" align="center"~~
	~~\|0 \|\| 0 \|\| 1 \|\| 1~~
	~~\|- bgcolor="#ddffdd" align="center"~~
	~~\|0 \|\| 1 \|\| 0 \|\| 1~~
	~~\|- bgcolor="#ddffdd" align="center"~~
	~~\|0 \|\| 1 \|\| 1 \|\| 0~~
	~~\|- bgcolor="#ddffdd" align="center"~~
	~~\|1 \|\| 0 \|\| 0 \|\| 0~~
	~~\|- bgcolor="#ddffdd" align="center"~~
	~~\|1 \|\| 0 \|\| 1 \|\| 0~~
	~~\|- bgcolor="#ddffdd" align="center"~~
	~~\|1 \|\| 1 \|\| 0 \|\| 0~~
	~~\|- bgcolor="#ddffdd" align="center"~~
	~~\|1 \|\| 1 \|\| 1 \|\| 0~~
	\|}

	~~Larger AOI gates~~, ~~such as 4-3 AOI~~ or ~~3-3-3 AOI~~ can ~~also be used~~.

	~~==Electronic implementation==~~
	~~[[File:CMOS 2~~-~~1AOI~~.~~svg\|thumb\|150px\|CMOS implementation~~ of ~~a 2-1 AOI gate]]~~
	~~AOI gates~~ can be ~~readily implemented in [[CMOS]] circuitry~~. ~~AOI gates~~ are ~~particularly advantaged in that~~ the ~~total number of transistors (~~or ~~gates) is less than if~~ the ~~AND, NOT,~~ and ~~OR functions were implemented separately. This results in increased speed,~~ reduced ~~power, smaller area, and potentially lower fabrication cost~~. ~~For example~~, ~~a 2-1 AOI gate~~ can ~~be constructed with 6 transistors in CMOS compared~~ to ~~10 transistors using~~ a ~~2-input NAND gate (4 transistors)~~, ~~an inverter (2 transistors), and a 2-input NOR gate (4 transistors)~~.

	~~== References ==~~
	~~{{reflist}}~~
	*{{cite book \|title=Engineering digital design: Revised Second Edition \|last = Tinder \|first=Richard F. ~~\|year=2000 \|isbn=0-12-691295-5 \|pages=317–319 \|url=~~http://~~books.google~~.com/~~books~~?id=~~6x0pjjMKRh0C&pg=PT347&lpg=PT347&dq=AOI+gate&source=web&ots=t-wt6hoi1-&sig=dlnF_Kq9jYe27dbr7Rb5gThgM2Y&hl=en&sa=X&oi=book_result&resnum=7&ct=result#PPT346~~,~~M1 \|accessdate=2008-07-04}}~~
	*{{cite book \|title=Application-Specific Integrated Circuits \|last=John \|first~~= Michael \|year=1997 \|url=~~http://~~iroi~~.~~seu.edu.cn/books/asics/Book2~~/~~CH02~~/~~CH02.4.htm#pgfId=799 \|accessdate= 2008~~-07-~~04}}~~

	~~[[Category:Logic gates\|AOI gate]~~]

195.205.223.7: /* Estimates based on expected entropy */

2014-01-16T12:38:23Z

Estimates based on expected entropy

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← Older revision		Revision as of 00:41, 30 September 2014
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	~~{{No footnotes\|date=April 2009}}[[File:AOI22Symbol.svg\|thumb\|250px\|right\|2-2 AOI Symbol]]~~
	~~[[File:AOI21Symbol.svg\|thumb\|250px\|right\|2-1 AOI Symbol]]~~

	'''AND-OR-Invert''' (AOI) logic and AOI gates are two-level compound (or complex) logic functions constructed from the combination of one or more [[AND gate]]s followed by a [[NOR gate]]. Construction of AOI cells is particularly efficient using [[CMOS]] technology where the total number of transistor gates can be compared to the same construction using [[NAND logic]] or [[NOR logic]]. The complement of AOI Logic is [[OR-AND-Invert]] (OAI) logic where the OR gates precede an AND gate.

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	~~AOI gates perform one~~ or ~~more [[logical~~ and~~\|AND]] operations followed by an [[logical~~ or~~\|OR]] operation~~ and ~~then an inversion~~. ~~For example~~, a ~~2-2 AOI gate~~ can be ~~represented by the [[Boolean algebra (logic)\|boolean equation]] and [[truth table]]:~~

	<~~math~~>~~F=\overline{(A \wedge B) \vee (C \wedge D)}~~<~~/math~~>

	~~{\| class=~~"~~wikitable~~"
	~~\|- bgcolor="#ddeeff" align="center"~~
	~~\|colspan=5\|2-2 AOI~~
	~~\|- bgcolor="#ddeeff" align="center"~~
	~~\|colspan=4\|'''INPUT~~'''<br>~~A   B   C   D \|\| '''OUTPUT'''~~<br> F
	~~\|- bgcolor="#ddffdd" align="center"~~
	~~\|0 \|\| X \|\| X \|\| 0 \|\| 1~~
	~~\|- bgcolor="#ddffdd" align="center"~~
	~~\|X \|\| 0 \|\| X \|\| 0 \|\| 1~~
	~~\|- bgcolor="#ddffdd" align="center"~~
	~~\|0 \|\| X \|\| 0 \|\| X \|\| 1~~
	~~\|- bgcolor="#ddffdd" align="center"~~
	~~\|X \|\| 0 \|\| 0 \|\| X \|\| 1~~
	~~\|- bgcolor="#ddffdd" align="center"~~
	~~\|1 \|\| 1 \|\| X \|\| X \|\| 0~~
	~~\|- bgcolor="#ddffdd" align="center"~~
	~~\|X \|\| X \|\| 1 \|\| 1 \|\| 0~~
	\|}

	~~A 2-1 AOI gate~~ can ~~be represented by following~~ the ~~boolean equation~~ and ~~truth table:~~

	<~~math~~>~~F=\overline{ A \vee~~ (~~B \wedge C~~)}<~~/math~~>

	~~{\| class="wikitable"~~
	~~\|- bgcolor="#ddeeff" align="center"~~
	~~\|colspan=4\|2-1 AOI~~
	~~\|- bgcolor="#ddeeff" align="center"~~
	~~\|colspan=3\|'''INPUT'''~~<br>~~A   B   C \|\| '''OUTPUT'''~~<br> F
	~~\|- bgcolor="#ddffdd" align="center"~~
	~~\|0 \|\| 0 \|\| 0 \|\| 1~~
	~~\|- bgcolor="#ddffdd" align="center"~~
	~~\|0 \|\| 0 \|\| 1 \|\| 1~~
	~~\|- bgcolor="#ddffdd" align="center"~~
	~~\|0 \|\| 1 \|\| 0 \|\| 1~~
	~~\|- bgcolor="#ddffdd" align="center"~~
	~~\|0 \|\| 1 \|\| 1 \|\| 0~~
	~~\|- bgcolor="#ddffdd" align="center"~~
	~~\|1 \|\| 0 \|\| 0 \|\| 0~~
	~~\|- bgcolor="#ddffdd" align="center"~~
	~~\|1 \|\| 0 \|\| 1 \|\| 0~~
	~~\|- bgcolor="#ddffdd" align="center"~~
	~~\|1 \|\| 1 \|\| 0 \|\| 0~~
	~~\|- bgcolor="#ddffdd" align="center"~~
	~~\|1 \|\| 1 \|\| 1 \|\| 0~~
	\|}

	~~Larger AOI gates~~, ~~such as 4-3 AOI~~ or ~~3-3-3 AOI~~ can ~~also be used~~.

	~~==Electronic implementation==~~
	~~[[File:CMOS 2~~-~~1AOI~~.~~svg\|thumb\|150px\|CMOS implementation~~ of ~~a 2-1 AOI gate]]~~
	~~AOI gates~~ can be ~~readily implemented in [[CMOS]] circuitry~~. ~~AOI gates~~ are ~~particularly advantaged in that~~ the ~~total number of transistors (~~or ~~gates) is less than if~~ the ~~AND, NOT,~~ and ~~OR functions were implemented separately. This results in increased speed,~~ reduced ~~power, smaller area, and potentially lower fabrication cost~~. ~~For example~~, ~~a 2-1 AOI gate~~ can ~~be constructed with 6 transistors in CMOS compared~~ to ~~10 transistors using~~ a ~~2-input NAND gate (4 transistors)~~, ~~an inverter (2 transistors), and a 2-input NOR gate (4 transistors)~~.

	~~== References ==~~
	~~{{reflist}}~~
	*{{cite book \|title=Engineering digital design: Revised Second Edition \|last = Tinder \|first=Richard F. ~~\|year=2000 \|isbn=0-12-691295-5 \|pages=317–319 \|url=~~http://~~books.google~~.com/~~books~~?id=~~6x0pjjMKRh0C&pg=PT347&lpg=PT347&dq=AOI+gate&source=web&ots=t-wt6hoi1-&sig=dlnF_Kq9jYe27dbr7Rb5gThgM2Y&hl=en&sa=X&oi=book_result&resnum=7&ct=result#PPT346~~,~~M1 \|accessdate=2008-07-04}}~~
	*{{cite book \|title=Application-Specific Integrated Circuits \|last=John \|first~~= Michael \|year=1997 \|url=~~http://~~iroi~~.~~seu.edu.cn/books/asics/Book2~~/~~CH02~~/~~CH02.4.htm#pgfId=799 \|accessdate= 2008~~-07-~~04}}~~

	~~[[Category:Logic gates\|AOI gate]~~]