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.

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

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.

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