What is fixed-point and floating point representation?

What is fixed-point and floating point representation?

Definition. Fixed point is a representation of real data type for a number that has a fixed number of digits after the radix point. Floating point is a formulaic representation of real numbers as an approximation so as to support a tradeoff between range and precision.

What is fixed point number system?

1 Fixed-Point Number Systems. Fixed-point notation has an implied binary point between the integer and fraction bits, analogous to the decimal point between the integer and fraction digits of an ordinary decimal number. The integer bits are called the high word and the fraction bits are called the low word.

What is fixed-point representation in digital electronics?

In fixed point notation, there are a fixed number of digits after the decimal point, whereas floating point number allows for a varying number of digits after the decimal point. This representation has fixed number of bits for integer part and for fractional part.

What is fixed-point representation?

In computing, fixed-point refers to a method of representing fractional (non-integer) numbers by storing a fixed number of digits of their fractional part. Dollar amounts, for example, are often stored with exactly two fractional digits, representing the cents (1/100 of dollar).

Where is fixed-point representation used?

Fixed point is a simple yet very powerful way to represent fractional numbers in computer. By reusing all integer arithmetic circuits of a computer, fixed point arithmetic is orders of magnitude faster than floating point arithmetic. This is the reason why it is being used in many game and DSP applications.

What are the advantages of floating-point representation?

Floating-point numbers have two advantages over integers. First, they can represent values between integers. Second, because of the scaling factor, they can represent a much greater range of values.

Is fixed-point faster than floating point?

Fixed point math, independent of processor speed, is easier to code with and faster than floating point math. Fixed point is adequate unless you know that you will be dealing with higher numbers than the fixed-point unit can handle. A floating-point number doesn’t have a fixed number of bits before and after a decimal.

What is the size of fixed-point integer?

In C, C++, and Java, floating-point variables are declared as float (32 bits) or double (64 bits), while integer fixed-point variables are declared as short int (typically 16 bits and never less), long int (typically 32 bits and never less), or simply int (typically the same as a long int, but sometimes between short …

What is fixed-point representation of integers?

Fixed point representation is used to store integers, the positive and negative whole numbers: … -3, -2, -1, 0, 1, 2, 3, …. High level programs, such as C and BASIC, usually allocate 16 bits to store each integer. In the simplest case, the 216 = 65,536 possible bit patterns are assigned to the numbers 0 through 65,535.

How do you calculate fixed-point representation?

In general, mathematically, given a fixed binary point position, shifting the bit pattern of a number to the right by 1 bit always divide the number by 2. Similarly, shifting a number to the left by 1 bit multiplies the number by 2.

What are the two main standards for floating-point representation?

There are three binary floating-point basic formats (encoded with 32, 64 or 128 bits) and two decimal floating-point basic formats (encoded with 64 or 128 bits). The binary32 and binary64 formats are the single and double formats of IEEE 754-1985 respectively.

What are the four essential elements of a number in floating-point notation?

The four essential elements of a number in floating-point notation are; sign, significand, exponent, base.

What do you call a fixed point representation?

This type of representation of a number as a string of digits with the decimal point in between two smaller strings (or groups) of digits is called as fixed-point representation. The group of digits to the left of decimal point is called as integer part, and those to the right of the decimal point is called as fractional (decimal) part.

How does a floating point number represent a fixed point number?

Instead it reserves a certain number of bits for the number (called the mantissa or significand) and a certain number of bits to say where within that number the decimal place sits (called the exponent). The floating number representation of a number has two part: the first part represents a signed fixed point number called mantissa.

Which is an example of a fixed point format?

In the fixed-point representation, the given number can now be written as Thus the range in this case will be between -31.96875 and +31.96875. We have: We find that in this case, the range (sometimes called the dynamic range) has been considerably decreased, but resolution has been greatly increased.

Which is an example of a digital number representation?

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.