Computer Science
Arithmetic Logic Unit
An Arithmetic Logic Unit (ALU) is a digital circuit that performs arithmetic and logical operations on binary numbers. It is a fundamental component of the central processing unit (CPU) of a computer and is responsible for performing arithmetic operations such as addition, subtraction, multiplication, and division, as well as logical operations such as AND, OR, and NOT.
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eBook - PDFEngineering Digital Design
Revised Second Edition
- Richard F. Tinder(Author)
- 2000(Publication Date)
- Academic Press(Publisher)
8.8 ARITHMETIC AND LOGIC UNITS As the name implies, the arithmetic and logic unit (ALU) is a universal combinational logic device capable of performing both arithmetic and logic operations. It is this versatility that makes the ALU an attractive building block in the central processing unit (CPU) of a computer or microprocessor. It is the object of this section to develop the techniques required to design and cascade ALU devices following three very different approaches: the dedicated ALU approach , the MUX approach , and the dual-rail approach with completion signals. The number and complexity of the operations that a given ALU can perform is a matter of the designer’s choice and may vary widely from ALU to ALU, as will be demonstrated in this section. However, the choice of operations is usually drawn from the list in Fig. 8.24. Other possible operations include zero, unity, sign-complement, magnitude comparison, parity generation, multiplication, division, powers, and shifting. Multiplication, division, and related operations such as arithmetic shifting are complex and are found only in the most sophisticated ALU chips. Also, the AND, OR, and XOR operations are often applied to complemented and uncomplemented operands, making possible a wide assortment of such operations. Presented in Fig. 8.25 is the block diagram symbol for a general n -bit slice ALU. This ALU accepts two n -bit input operands, B n − 1 · · · B 1 B 0 and A n − 1 · · · A 1 A 0 , and a carry-in bit, C in , and operates with them in some predetermined way to output an n -bit function, F n − 1 · · · F 1 F 0 and a carry-out bit, C out . Here, the term n-bit slice indicates a partition of identical n -bit modules of stages that can be cascaded in parallel. Thus, an FA in an n -bit R-C adder could be called a 1-bit slice for that adder. Also, use of sign-complement arith-metic avoids the need for both carry and borrow parameters.
eBook - PDFEmbedded DSP Processor Design
Application Specific Instruction Set Processors
- Dake Liu(Author)
- 2008(Publication Date)
- Morgan Kaufmann(Publisher)
CHAPTER 12 ALU HW Implementation A datapath in a DSP processor typically consists of ALU, MAC, RF, and instruction-level acceleration units. In this chapter, implementation of the ALU hardware will be discussed based on examples. 12.1 ARITHMETIC AND LOGIC UNIT (ALU) In a real DSP processor, an ALU could cover more functions such as shift-rotation functions, bit manipulation functions, and some application-specific functions. ALU gets operands from a RF and sends results to a RF. Usually an ALU executes only RISC instructions, meaning that all operands to ALUs are from RFs,and the execution cost of each ALU instruction is one clock cycle. Iterative instructions are assigned to a MAC unit. In most cases, ALU operands and results are with native data width (the data width of register and memory bus). Double-precision computing usually is executed in a MAC unit. Figure 12.1 gives a top view of an ALU. Two 16-bit inputs are selected for ALU. Inputs of an ALU can be from the register file (RF) and as immediate data from the control path and carried by an instruction. The preprocessing of operand A and operand B includes guard insertion, operand inversion, and preparing for the carry-in. After preprocessing, operands will be shared by all the processing units, including the arithmetic unit, the shift unit, the logic unit, and the special function unit. Each processing unit gives computing on the same operands after preprocess-ing. One of the outputs from processing units will be selected for postprocessing. The postprocessing includes saturation on the result and the flag computing. AnALU could be part of the MAC in an early DSP processor in the 1980s when gate count was critical. Today, the silicon cost is not so expensive when using modern silicon technology. For example, by using a 65-nanometer digital CMOS process, more than 200 k gates or 400 k bits memory cells can be allocated within 1 mm 2 .The silicon cost of an ALU of a 16-bit DSP processor is less than 5 k gates.
eBook - PDF- Miloš D. Ercegovac, Tomás Lang, Miloš D. Ercegovac(Authors)
- 2003(Publication Date)
- Morgan Kaufmann(Publisher)
CHAPTER I Review of Basic Number Representations and Arithmetic Algorithms In this chapter we briefly review basic number representations and algorithms used in digital arithmetic. The treatment is very concise; readers that need a more detailed review should consult some of the references listed at the end of the chapter. More advanced algorithms as well as the implementations are the topic of later chapters. 1.1 Digital Arithmetic and Arithmetic Units Digital arithmetic encompasses the study of number representations, algorithms for operations on numbers, implementations of arithmetic units in hardware, and their use in general-purpose and application-specific systems. An arithmetic unit (processor) is a system that performs operations on num- bers. We limit ourselves to the most common cases in which these numbers are 1. fixed-point numbers 9 integersI = {-N,..., N} 9 rational numbers of the form x = a/2f (binary rationals), a ~ I and f positive integer floating-point numbers x • b E, x rational number, b the integer base, and E integer exponent. The floating-point numbers approximate real numbers and facilitate computations over a wide dynamic range. Collectively, we refer to these numbers as DA (digital arithmetic) numbers. . 4 c HA P T E R I Review of Basic Number Representations and Arithmetic Algorithms An arithmetic processor operates on one, two, or more operands depending on the operation. The operands are characterized by a representation and a set of values as defined in the next section. The operation is selected from an allowable set, which usually includes addition, subtraction, multiplication, division, square root, change of sign, comparison, and so on. The results can be DA numbers, logical variables (conditions), and/or singularity conditions (exceptions). Logical results occur for operations such as comparison, check for zero, and the like.
eBook - PDFAn Introduction to Digital Computing
Pergamon Programmed Texts
- F. H. George(Author)
- 2014(Publication Date)
- Pergamon(Publisher)
Inside our computer, as well as having a storage, you will remember that we also have an arithmetic unit which provides the usual means for adding, subtracting and such like arith-metical operations. We must now remind you of the analogy which you should bear in mind. Inside the computer we have a control unit, which is like a signal box in a railway system. It organizes the controls, the flow of (trains) information, and where the trains stop is the railway station. In computer language, the railway station is the address of the word, which may contain either instructions or numbers. Are all the instructions arithmetical? Turn to 108 100 106 from 104 The S.C.R. adds 1 to the address and transforms 246 into 247. So you are not correct. To see what was said to those who were correct, go to 102 107 from 101 The control unit (CU.) is composed of the instruction register (I.R.) and the sequence control register (S.C.R.). So our statement was true and you were wrong. Go to 104 from 105 No. There are organizational and input-output instructions as well as arithmetical instructions. We have said that computer words are represented by com-binations of holes punched on tape or card, for the purpose of input and output. Inside the computer, these punched holes are translated into electrical pulses, which travel from input to the store, and from the store to the arithmetic unit, back to the store to the output, and a copy to the store, and so on and so forth. It is all very much like a network of railway lines, where the word-pulses are the trains. The C.U. has the job of sending these trains to the right place at the right time. Indeed, the process does seem fairly com-plicated—but only at first sight. What does the I.R. contain? Turn to 109 100 109 from 108 The LR. contains the instruction currently being obeyed. Now for a little revision. A digital computer is made up primarily as follows.
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