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Numerical Representation and Analysis

Numerical Representation and Analysis - Numerical...

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Numerical Representation and  Analysis For RC App Designs
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Numerical Representations Order of preference 1. Integer 2. Fixed-point  3. FP Floating-point (single-precision) 4. FP Floating-point (double-precision) Integer representation Advantages:  o. Very efficient hardware implementations (data paths, storage, etc.) o. Basic operations (add, subtract, multiply, etc.) are inexpensive (wrt.  area, speed, power) Disadvantages, some applications cannot use  integer representation, e.g., o. Need fractional values
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Fixed-Point Representation +118.625  in 8.8 format =  0111 0110^1010 0000 - 118.625  in 8.8 format (2’s complement) 1000 1001^0101 1111   + 1 =  1000 1001^0110 0000 Comparison to Floating-Point representation Exponent is fixed o Dynamic range is reduced o But, no need for alignment (barrel shifter) Basic math operations essentially identical to those of  integer ops o Low area usage o Lower power
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Floating-Point (FP) Adder
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