Floating Point Unit (FPU)
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Floating point unit (FPU) digital signal processing includes fixed and floating point formats for number manipulation in computing, with three types: half precision, single precision, and double precision. FPUs perform arithmetic operations on floating point numbers and are necessary for complex computations, particularly in applications like image processing that require high precision and processing speed. Power-optimized designs using logarithmic number systems can significantly reduce energy consumption in battery-operated devices.
Floating Point Unit (FPU)
- 1. FLOATING PINT UNIT (FPU) Digital signal processing can be divided into two subcategories, fixed point and floating points. These are the formats refer to store and manipulate numbers within the devices. In computing, floating point is a method of representing an approximation of a real number in a way that can support a trade-off between range and precision. A number that can be represented exactly is of the following form: There are three types of floating point numbers:-half precision, single precision and double precision. Half precision-Half precision floating point is a 16-bit binary floating-point interchange format. From 16 bits, 15th bit is used for sign bit, 14th to 10th bit is used for exponent part and remaining 10 bits are used to represent significand bits. Single precision- total 32 bits are used to represent single precision floating point number. 31st bit is used for sign bit, 30th to 23rd bits are used for exponent part and remaining 23 bits are used for significant part. Double precision- total 64 bits are used to represent single precision floating point number. 63rd bit is used for sign bit, 62th to 52th bits are used for exponent part and remaining bits are used for significand part.
- 2. Floating point unit- floating point unit is an IC which is designed to manipulate all the arithmetic operations based on floating point numbers or fractions. This unit is fully dedicated to work only on floating point numbers and nothing else. The basic microprocessor is not capable of manipulating floating number quickly so a separate specialized floating point unit is designed as coprocessor. This unit is designed to perform basically five operations:- 1. Addition 2. Subtraction 3. Multiplication 4. Division 5. Square root If we take an example of FPU application that is an image processing system which uses a lossy biorthogonal 9/7 lifting DWT technique and this yields a problem of complex computations with floating point numbers. Such a system requires an additional hardware to handle the floating point computations. This leads to design of a separate floating point unit. Example of floating point addition:- Let’s we have two 5 digit binary numbers 24*1.1001 + 22*1.0010
- 3. Step1- Find the difference between larger and smaller exponent. El=24, Es =22, difference=4-2=2 Step 2- makes the exponent equal by shifting the fraction with the smaller exponent right by the difference bits (2). And add both fractions 1.1001 000 +0.0100 100 1.1101 100 Step 3- round the result to nearest even 1.1110 Result= 24*1.1110 Similarly other operations can also be computed using FPU. There are operational switches on the FPU, on the bases of input given to switch it decides which operation is going to be performed. If adder operator is fed to the switch then addition operation will be take place. Same procedure is followed for subtraction, multiplication, division and square root. We can use this FPU in many VLSI applications such as power optimized image processing system. To reduce the power consumption we use logarithmic based FPU instead of conventional FPU. Today’s image acquiring tools are generally battery operated and hence optimization of power is a major concern. Using LNS (logarithmic number system) in arithmetic unit results in reduced power. For More Any Query You Can Visit Us At: http://www.siliconmentor.com/