Data Types and Scaling in Digital Hardware

In digital hardware, numbers are stored in binary words. A binary word is a fixed-length sequence of binary digits (1's and 0's). The way in which hardware components or software functions interpret this sequence of 1's and 0's is described by a data type.

Binary numbers are represented as either fixed-point or floating-point data types. A fixed-point data type is characterized by the word size in bits, the binary point, and whether it is signed or unsigned. The binary point is the means by which fixed-point values are scaled. With the Fixed-Point Designer™ software, fixed-point data types can be integers, fractionals, or generalized fixed-point numbers. The main difference between these data types is their default binary point.

Floating-point data types are characterized by a sign bit, a fraction (or mantissa) field, and an exponent field. Fixed-Point Designer adheres to the IEEE® Standard 754-1985 for Binary Floating-Point Arithmetic (referred to simply as the IEEE Standard 754 throughout this guide) and supports singles and doubles.

When choosing a data type, you must consider these factors:

  • The numerical range of the result

  • The precision required of the result

  • The associated quantization error (i.e., the rounding mode)

  • The method for dealing with exceptional arithmetic conditions

These choices depend on your specific application, the computer architecture used, and the cost of development, among others.

With the Fixed-Point Designer software, you can explore the relationship between data types, range, precision, and quantization error in the modeling of dynamic digital systems. With the Simulink® Coder™ product, you can generate production code based on that model. With HDL Coder™, you can generate portable, synthesizable VHDL and Verilog code from Simulink models and Stateflow® charts.

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