# Fixed Point And Floating Point Number Representations Pdf File

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- A Tutorial on Data Representation
- Fixed-Point and Floating-Point Basics
- Select a Web Site
- Fixed-point arithmetic

## A Tutorial on Data Representation

Human beings use decimal base 10 and duodecimal base 12 number systems for counting and measurements probably because we have 10 fingers and two big toes. Computers use binary base 2 number system, as they are made from binary digital components known as transistors operating in two states - on and off. In computing, we also use hexadecimal base 16 or octal base 8 number systems, as a compact form for representing binary numbers. Decimal number system has ten symbols: 0 , 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , and 9 , called digit s. It uses positional notation. For example,. Binary number system has two symbols: 0 and 1 , called bits.

Documentation Help Center. In digital hardware, numbers are stored in binary words. A binary word is a fixed-length sequence of bits 1s and 0s. How hardware components or software functions interpret this sequence of 1s and 0s is defined by the data type. Binary numbers are represented as either fixed-point or floating-point data types.

Double-precision floating-point format sometimes called FP64 or float64 is a computer number format , usually occupying 64 bits in computer memory; it represents a wide dynamic range of numeric values by using a floating radix point. Floating point is used to represent fractional values, or when a wider range is needed than is provided by fixed point of the same bit width , even if at the cost of precision. Double precision may be chosen when the range or precision of single precision would be insufficient. IEEE specifies additional floating-point formats, including bit base-2 single precision and, more recently, base representations. One of the first programming languages to provide single- and double-precision floating-point data types was Fortran. Before the widespread adoption of IEEE , the representation and properties of floating-point data types depended on the computer manufacturer and computer model, and upon decisions made by programming-language implementers. Double-precision binary floating-point is a commonly used format on PCs, due to its wider range over single-precision floating point, in spite of its performance and bandwidth cost.

## Fixed-Point and Floating-Point Basics

In computing , a fixed-point number representation is a real data type for a number that has a fixed number of digits after and sometimes also before the radix point after the decimal point '. Fixed-point number representation can be compared to the more complicated and more computationally demanding floating-point number representation. Fixed-point numbers are useful for representing fractional values , usually in base 2 or base 10, when the executing processor has no floating point unit FPU as is the case for older or low-cost embedded microprocessors and microcontrollers , if fixed-point provides improved performance or accuracy for the application at hand, or if their use is more natural for the problem such as for the representation of angles. A value of a fixed-point data type is essentially an integer that is scaled by an implicit specific factor determined by the type. For example, the value 1.

Digital Computers use Binary number system to represent all types of information inside the computers. Alphanumeric characters are represented using binary bits i. Digital representations are easier to design, storage is easy, accuracy and precision are greater. There are various types of number representation techniques for digital number representation, for example: Binary number system, octal number system, decimal number system, and hexadecimal number system etc. But Binary number system is most relevant and popular for representing numbers in digital computer system. There are two major approaches to store real numbers i.

Documentation Help Center. In digital hardware, numbers are stored in binary words. A binary word is a fixed-length sequence of bits 1's and 0's. The way hardware components or software functions interpret this sequence of 1's and 0's is defined by the data type. Binary numbers are represented as either floating-point or fixed-point data types. In this section, we discuss many terms and concepts relating to fixed-point numbers, data types, and mathematics.

[QF] format fixed-point number format analyzed in this paper is broken down in subsequent compiler support for double precision floating-point numbers. Floating-point childrenspolicycoalition.org 2.

## Select a Web Site

In real life, we deal with real numbers -- numbers with fractional part. Most modern computer have native hardware support for floating point numbers. However, the use of floating point is not necessarily the only way to represent fractional numbers. This article describes the fixed point representation of real numbers.

*Copyright , Association for Computing Machinery, Inc. Floating-point arithmetic is considered an esoteric subject by many people. This is rather surprising because floating-point is ubiquitous in computer systems.*

### Fixed-point arithmetic

The standard addressed many problems found in the diverse floating-point implementations that made them difficult to use reliably and portably. Many hardware floating-point units use the IEEE standard. The first standard for floating-point arithmetic, IEEE , was published in It covered only binary floating-point arithmetic. The binary formats in the original standard are included in this new standard along with three new basic formats, one binary and two decimal.

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A fixed-point representation of a number may be thought to consist of 3 parts: the sign field, integer field, and fractional field. One way to store a number using a bit format is to reserve 1 bit for the sign, 15 bits for the integer part and 16 bits for the fractional part.

These are (i) Fixed Point Notation and (ii) Floating Point Notation. In fixed point notation, there are a fixed number of digits after the decimal.