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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