The Art of the Helicopter John Watkinson - Karatunov.net

300 The Art of the Helicopter
Fig. 7.37 Two’s complement coding. See text for details.
In the two’s complement system, the upper half of the pure binary number range has
been redefined to represent negative quantities. If a pure binary counter is constantly
incremented and allowed to overflow, it will produce all the numbers in the range
permitted by the number of available bits, and these are shown for a four-bit example
drawn around the circle in Figure 7.37. As a circle has no real beginning, it is possible
to consider it to start wherever it is convenient. In two’s complement, the quantizing
range represented by the circle of numbers does not start at zero, but starts on the
diametrically opposite side of the circle. Zero is midrange, and all numbers with the
MSB set are considered negative. The MSB is thus the equivalent of a sign bit where
1 = minus. Two’s complement notation differs from pure binary in that the most
significant bit is inverted in order to achieve the half circle rotation.
Controls having limited travel, such as potentiometers and LDVTs, can also have
their outputs converted to two’s complement. Figure 7.38 shows how a real ADC
(analog to digital convertor) is configured to produce two’s complement output from,
for example, a potentiometer. At (a) an analog offset voltage equal to one-half the
quantizing range is added to the bipolar analog signal in order to make it unipolar as
at (b). The ADC produces positive only numbers at (c) which are proportional to the
input voltage. The MSB is then inverted at (d) so that the all-zeros code moves to the
centre of the quantizing range. The analog offset is often incorporated in the ADC as
is the MSB inversion. Some encoders are designed to be used in either pure binary or
two’s complement mode where the MSB inversion may be applied as required.