L2330 datasheet(5/14 Pages) LODEV

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DEVICES INCORPORATED

Special Arithmetic Functions

L2330

Coordinate Transformer

09/27/2001–LDS.2330-E

32767

65535

π/2

Conversion Ranges

The L2330 supports 16-bit unsigned

radii and 16-bit signed Cartesian

coordinates. Since the 16-bit rectangular

coordinate space does not completely

cover the polar space defined by 16-bit

radii, certain values of “r” will not map

correctly. This condition is indicated by

the overflow (OVF) flag.

In Polar-to-Rectangular conversions, no

overflow occurs for r

≤ 32767 (7FFFH).

Overflow will always occur when r >

46341 (B505H). Note that in signed

magnitude mode r = 46340 (B504H)

will also cause an overflow. For 32767

≤

≤ 46340, overflow may occur depend-

ing on the exact values of r and

θ.

Figure 2 shows, for the first quadrant,

these three regions: A = no overflow

(correct conversion), B = possible

overflow, C = overflow. The other

quadrants are mapped in a similar

manner.

When in signed magnitude mode, the

overflows on the other three quadrants

are the same as in the first. This occurs

because the signed magnitude number

system is symmetric about zero. For

example, if a given r and angle

θ cause

an overflow, the same r will cause an

overflow for the angles -

θ, π+θ , π-θ.

However, when in two’s complement

mode, the overflows aren’t quite the

same. This occurs because the two’s

FIGURE 2.

CONVERSION RANGES

complement number system is not

symmetric about zero. For example, if

the X or Y component of the input is

–32768 (8000H), no overflow occurs.

But if the X or Y component of the

input is +32768, overflow does occur.

When converting from Rectangular-to-

Polar, if both inputs are zero the radius

is zero but the angle is not defined.

The L2330 will output 4707H in this

case. Since the angle is not defined for a

zero length vector, this is not an error.

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