AN2388 datasheet(37/54 Pages) STMICROELECTRONICS

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AN2388

Software design

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4.4.2

Numerical considerations

The PU model has been developed in order to represent some quantities that reach nominal

value in certain condition. Take into consideration that during the transient the current might

reach higher values than the nominal current (Ib).

The numeric format consideration

Integer data is inherently represented as a signed two’s complement value, where the most

significant bit is defined as a sign bit. Generally, the range of an N-bit two’s complement

integer is -2N-1 to 2N-1-1. For a 16-bit integer, the data range is -32768 (0x8000) to 32767

(0x7FFF), including 0. Fractional data is represented as a two’s complement number where

the most significant bit is defined as a sign bit, and the radix point is implied to lie just after

the sign bit. This format is commonly referred to as 1.15 (or Q15) format, where 1 is the

number of bits used to represent the integer portion. The range of an N-bit two’s

complement fraction with this implied radix point is -1.0 to (1-21-N). For a 16-bit fraction, the

1.15 data range is -1.0 (0x8000) to 0.999969482 (0x7FFF), including 0.0 .

The resolution in this format is:

In normal saturation mode, the 32-bit accumulators use a 1.31 format, which enhances the

precision to 4.6566*10-10.

An example of different representations (positive and negative numbers) are shown below:

4.4.3

ST10-DSP features

ST10 is a combined CPU and DSP.

As a CPU, it is a powerful real time oriented 16-bit CPU.

As a DSP, it is a single MAC 16 by 16-bit multiplier with a 40-bit accumulator

01518

−

000000000000

-20 2-1

2-15

Implied radix point

0x4001 = 2-1 + 2-15 = 0.000301518 = 0.500301518

1.15 Fractional Format

0000000

000010

-20 2-1

2-15

Implied radix point

0xC002 = -20 + 2-1 + 2-14 = -1.0 + 0.5 + 0.000061035 = -0.499938965

1.15 Fractional Format (negative number)

2-14

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