Lecture 14

Digital System Design

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Floating & Fixed Point Arithmetic

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Two Types of arithmetic

Floating Point Arithmetic Used where precision and dynamic range are important Most algorithms are developed in FP Ease of coding More Cost (Area, Speed, Power)

Fixed Point Arithmetic Place of decimal is fixed Simpler HW, low power, less silicon Converting FP simulation to Fixed-point simulation is time consuming The code is less readable, need to worry about overflow and scaling issues

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Fixed-point v/s Floating-point Hardware

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Algorithms are developed in floating point format using tools

like Matlab

Floating point processors and HW are expensive

Fixed-point processors and HW are used in embedded

systems

After algorithms are designed and tested then they are

converted into fixed-point implementation

The algorithms are ported on Fixed-point processor or

application specific hardware

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Number Representation

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In a digital design fixed or floating point numbers are

represented in binary format Types of Representation

ones complement

sign magnitude

canonic sign digit (CSD)

twos complement

In digital system design for fixed point implementation the

canonic sign digit (CSD), and twos complement are

normally used

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IEEE-754 64-bit Double-Precision Floating-

Point Numbers

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Floating Point Addition/Subtraction

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Fixed Point Arithmetic

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Best way to learn DSD is to do it!

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