MATLAB EMBEDDED IDE LINK 4 - FOR USE WITH TEXAS INSTRUMENTS CODE COMPOSER STUDIO Podręcznik Użytkownika Pobierz pdf (Strona 37)

Fixed-Point Numbers

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Fixed-Point Numbers

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). How hardware components

or software functions interpret this sequence of 1’s and 0’s is defined by the

data type.

Binary numbers are used to represent 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 position of the binary

point is the means by which fixed-point values are scaled and interpreted.

For example, a binary representation of a fractional fixed-point number (either

signed or unsigned) is shown below.

where

• is the ith binary digit.

• is the word size in bits.

• is the location of the most significant (highest) bit (MSB).

• is the location of the least significant (lowest) bit (LSB).

• The binary point is shown four places to the left of the LSB. In this example,

therefore, the number is said to have four fractional bits, or a fraction length

of four.

Signed Fixed-Point Numbers

Signed binary fixed-point numbers are typically represented in one of three

ways:

• Sign/magnitude

• One’s complement

• Two’s complement

•

…

ws 2–

ws 1–

MSB LSB

binary point

ws 1–

1 2 ... 32 33 34 35 36 37 38 39 40 41 42 ... 111 112

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MATLAB EMBEDDED IDE LINK 4 - FOR USE WITH TEXAS INSTRUMENTS CODE COMPOSER STUDIO Podręcznik Użytkownika Strona 37