MATLAB EMBEDDED IDE LINK 4 - FOR USE WITH TEXAS INSTRUMENTS CODE COMPOSER STUDIO Podręcznik Użytkownika Pobierz pdf (Strona 38)

2 Using the IQmath Library

2-4

Two’s complement is the most common representation of signed fixed-point

numbers and is used by TI digital signal processors.

Negation using signed two’s complement representation consists of a bit

inversion (translation into one’s complement) followed by the binary addition

of a 1. For example, the two’s complement of 000101 is 111011, as follows:

000101 ->111010 (bit inversion) ->111011 (binary addition of a 1 to the LSB)

Q Format Notation

The position of the binary point in a fixed-point number determines how you

interpret the scaling of the number. When it performs basic arithmetic such as

addition or subtraction, hardware uses the same logic circuits regardless of the

value of the scale factor. In essence, the logic circuits have no knowledge of

a binary point. They perform signed or unsigned integer arithmetic — as if the

binary point is to the right of b

. Therefore, you determine the binary point.

In the IQmath Library, the position of the binary point in the signed,

fixed-point data types is expressed in and designated by Q format notation.

This fixed-point notation takes the form

Qm.n

where

• designates that the number is in Q format notation — the Texas

Instruments representation for signed fixed-point numbers.

• is the number of bits used to designate the two’s complement integer

portion of the number.

• is the number of bits used to designate the two’s complement fractional

portion of the number, or the number of bits to the right of the binary point.

In Q format, the most significant bit is always designated as the sign bit.

Representing a signed fixed-point data type in Q format always requires

m+n+1 bits to account for the sign.

Example — Q.15

For example, a signed 16-bit number with n = 15 bits to the right of the binary

point is expressed as

Q0.15

1 2 ... 33 34 35 36 37 38 39 40 41 42 43 ... 111 112

Brak uwag

MATLAB EMBEDDED IDE LINK 4 - FOR USE WITH TEXAS INSTRUMENTS CODE COMPOSER STUDIO Podręcznik Użytkownika Strona 38