# Alu181

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Arithmetic logic unit

Arithmetic Logic Unit schematic symbol

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 microprocessorscontain one for purposes such as maintaining timers. The processors found inside modern CPUs and graphics processing units (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 animportant part of computer science, falling under Arithmetic and logic structures in the ACM Computing Classification System.
Contents [hide]
1 Numerical systems
2 Practical overview
2.1 Simple operations
2.2 Complex operations
2.3 Inputs and outputs
2.4 ALUs vs. FPUs
4 Notes
5 References
Numerical systems

Main article: Signed numberrepresentations
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 ones' complement, two's complement sign-magnitude format, and even true decimal systems, with various[NB 2] representation of the digits. ALUs foreach one of these that makes it easier for the ALUs to calculate additions and subtractions.[citation needed]
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 requiresadding 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 input registers, an external Control Unit then tells the ALUwhat 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

A simple example arithmetic logic unit (2-bit ALU) that does AND, OR, XOR, and addition
Most ALUs can perform the following operations:
Bitwise logic operations (AND,NOT, OR, XOR)
Integer arithmetic operations (addition, subtraction, and sometimes multiplication and division, though this is more expensive)
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 anArithmetic Logic Unit to calculate any 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:
Calculationin 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...