L2330 View Datasheet(PDF) - LOGIC Devices
Part Name
Description
MFG CO.
'L2330' PDF : 14 Pages View PDF
DEVICES INCORPORATED
L2330
Coordinate Transformer
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.
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.
FIGURE 2. CONVERSION RANGES
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.
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 ≤
r ≤ 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.
π/2
65535
32767
C
B
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
A
y
r
θ
x
32767
65535
Special Arithmetic Functions
5
09/27/2001–LDS.2330-E
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