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[[Image:ALU symbol.svg|right|thumb|Arithmetic Logic Unit schematic symbol]]
[[Image:KL Texas Instruments ALU SN74AS888.jpg|right|thumb|180px|Cascadable 8 Bit ALU Texas Instruments SN74AS888]]

In [[computing]], an '''arithmetic logic unit''' ('''ALU''') is a [[digital circuit]] that performs [[arithmetic]] and [[logical]] operations. 
The ALU is a fundamental building block of the [[central processing unit]] of a computer, and even the simplest [[microprocessor]]s contain one for purposes such as maintaining timers. The processors found inside modern CPUs and graphics processing units ([[Graphics processing unit|GPUs]]) accommodate very powerful and very complex ALUs; a single component may contain a number of ALUs.

Mathematician [[John von Neumann]] proposed the ALU concept in 1945, when he wrote a report on the foundations for a new computer called the [[EDVAC]].  Research into ALUs remains an important part of [[computer science]], falling under '''Arithmetic and logic structures''' in the [[ACM Computing Classification System]].

==Numerical systems==
{{Main|Signed number representations}}
An ALU must process numbers using the same format as the rest of the digital circuit. The format of modern processors is almost always the [[two's complement]] binary number representation. Early computers used a wide variety of number systems, including [[Signed number representations#Ones' complement|ones' complement]], [[Signed number representations#Two's complement|two's complement]] [[Signed number representations#Sign-and-magnitude method|sign-magnitude]] format, and even true decimal systems, with various{{#tag:ref|Including Binary-Coded Decimal (BCD) in 4 bits, 2-out-of-5 coding in five bits<ref>[http://bitsavers.org/pdf/ibm/7070/A22-7003-01_7070_Reference_Jan60.pdf Reference Manual, 7070 Data Processing System, A22-7003-01]</ref>, 5-bit biquinary<ref name=biquinary group=NB>IBM and UNIVAC used the term biquinqary with different meanings.</ref> encoding<ref>[http://bitsavers.org/pdf/univac/uss/SolidState90_Specs.pdf UNIVAC SOLID-STATE
90 Specification Features]</ref>, and 2-out-of-seven biquinary<ref name=biquinary group=NB/> encoding in 7 bits<ref>[http://bitsavers.org/pdf/ibm/650/22-6060-2_650_OperMan.pdf 650 Data Procssing Machine Manual of Operation, 22-6060-2]</ref>|name=name|group=NB}} representation of the digits.
ALUs for each one of these that makes it easier for the ALUs to calculate additions and subtractions.{{Citation needed|date=October 2007}}

The ones' complement and two's complement number systems allow for subtraction to be accomplished by adding the negative of a number in a very simple way which negates the need for specialized circuits to do subtraction; however, calculating the negative in two's complement requires adding a one to the low order bit and propagating the carry. An alternative way to do two's complement subtraction of A−B is to present a one to the carry input of the adder and use ¬B rather than B as the second input.

==Practical overview==

Most of a processor's operations are performed by one or more ALUs. An ALU loads data from [[processor register|input register]]s, an external [[Control Unit]] then tells the ALU what operation to perform on that data, and then the ALU stores its result into an output register. The [[Control Unit]] is responsible for moving the processed data between these registers, ALU and memory.

===Simple operations===
[[Image:2-bit ALU.svg|right|thumb|A simple example arithmetic logic unit (2-bit ALU) that does AND, OR, XOR, and addition]]
Most ALUs can perform the following operations:

*[[Bitwise operation|Bitwise logic operations]] ([[AND gate|AND]], [[NOT gate|NOT]], [[OR gate|OR]], [[NOR gate|XOR]])
*[[Integer (computer science)|Integer]] arithmetic operations ([[addition]], [[subtraction]], and sometimes [[multiplication]] and [[Division (mathematics)|division]], though this is more expensive)
*[[Bitwise operation#Bit shifts|Bit-shifting]] operations (shifting or rotating a word by a specified number of bits to the left or right, with or without [[sign extension]]). Shifts can be seen as multiplications and divisions by a [[power of two]].

===Complex operations===
Engineers can design an Arithmetic Logic Unit to calculate any<!-- anything at all?? --> operation. The more complex the operation, the more expensive the ALU is, the more space it uses in the processor, the more power it dissipates. Therefore, engineers compromise. They make the ALU powerful enough to make the processor fast, yet not so complex as to become prohibitive. For example, computing the square root of a number might use:

# '''Calculation in a single clock''' Design an extraordinarily complex ALU that calculates the square root of any number in a single step.
# '''Calculation pipeline''' Design a very complex ALU that calculates the square root of any number in several steps. The intermediate results go through a series of circuits arranged like a factory production line. The ALU can accept new numbers to calculate even before having finished the previous ones. The ALU can now produce numbers as fast as a single-clock ALU, although the results start to flow out of the ALU only after an initial delay.
# '''Iterative calculation''' Design a complex ALU that calculates the square root through several steps. This usually relies on control from a complex [[control unit]] with built-in [[microcode]].
# '''Co-processor''' Design a simple ALU in the processor, and sell a separate specialized and costly processor that the customer can install just beside this one, and implements one of the options above.
# '''Software libraries''' Tell the programmers<!-- who am "I" supposed to be here? --> that there is no [[co-processor]] and there is no [[emulator|emulation]], so they will have to write their own algorithms to calculate square roots by software.
# '''Software emulation''' [[Emulate]] the existence of the [[co-processor]], that is, whenever a program attempts to perform the square root calculation, make the processor check if there is a [[co-processor]] present and use it if there is one; if there isn't one, [[interrupt]] the processing of the program and invoke the [[operating system]] to perform the square root calculation through some software algorithm.

The options above go from the fastest and most expensive one to the slowest and least expensive one. Therefore, while even the simplest computer can calculate the most complicated formula, the simplest computers will usually take a long time doing that because of the several steps for calculating the formula.

Powerful processors like the [[Intel Core]] and [[AMD64]] implement option #1 for several simple operations<!-- such as? -->, #2 for the most common complex operations<!-- like? --> and #3 for the extremely complex operations<!-- ? -->.

===Inputs and outputs===
The inputs to the ALU are the data to be operated on (called [[operand]]s) and a code from the [[control unit]] indicating which operation to perform. Its output is the result of the computation.

In many designs the ALU also takes or generates as inputs or outputs a set of condition codes from or to a [[status register]].  These codes are used to indicate cases such as [[carry (arithmetic)|carry]]-in or carry-out, [[arithmetic overflow|overflow]], [[division by zero|divide-by-zero]], etc.<!-- <ref name="Stallings page 290-291"/> -->


A [[floating-point unit]] also performs arithmetic operations between two values, but they do so for numbers in [[Floating point|floating-point]] representation, which is much more complicated than the [[two's complement]] representation used in a typical ALU. In order to do these calculations, a [[Floating-point unit|FPU]] has several complex circuits built-in, including some internal ALUs.

In modern practice, engineers typically refer to the ALU as the circuit that performs integer arithmetic operations (like [[two's complement]] and [[Binary-coded decimal|BCD]]). Circuits that calculate more complex formats like [[floating point]], [[complex numbers]], etc. usually receive a more specific name such as FPU.

==See also==
*[[7400 series]]
*[[74181]]
*[[Adder (electronics)]]
*[[Multiplication ALU]]
*[[Digital circuit]]
*[[Division (electronics)]]
*[[Control Unit]]

==Notes==
{{Reflist|group=NB}}

==References==
<!--This article uses the Cite.php citation mechanism. If you would like more information on how to add footnotes to this article, please see http://meta.wikimedia.org/wiki/Cite/Cite.php -->
{{Reflist}}
*{{Cite book | first=Enoch| last=Hwang| year=2006| title=Digital Logic and Microprocessor Design with VHDL| publisher=Thomson| isbn=0-534-46593-5| url=http://faculty.lasierra.edu/~ehwang/digitaldesign| authorlink=Enoch Hwang}}
*{{Cite book | first=William| last=Stallings| year=2006| title=Computer Organization & Architecture: Designing for Performance 7th ed| publisher=Pearson Prentice Hall| isbn=0-13-185644-8| url=http://williamstallings.com/COA/COA7e.html| authorlink=William Stallings}}

==External links==
*[http://www.mathworks.com/matlabcentral/fileexchange/loadFile.do?objectId=12762&objectType=FILE A Simulator of Complex ALU in MATLAB]
*[http://www.youtube.com/watch?v=LGkkyKZVzug&objectType=FILE An ALU implemented in Minecraft]

{{CPU technologies}}

{{DEFAULTSORT:Arithmetic Logic Unit}}
[[Category:Digital circuits]]
[[Category:Central processing unit]]
[[Category:Computer arithmetic]]
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