Information Technology Reference
In-Depth Information
waveform suffers a shifted baseline. This problem can be overcome with digital luminance signals simply by
subtracting the offset from each sample before processing as this results in positive-only numbers truly proportional
to the luminance voltage. This approach is not suitable for audio or colour difference signals because negative
numbers would result when the analog voltage goes below blanking and pure binary coding cannot handle them.
Figure 2.36:
The result of an attempted attenuation in pure binary code is an offset. Pure binary cannot be used for
digital audio processing.
The problem with offset binary is that it works with reference to one end of the range. What is needed is a
numbering system which operates symmetrically with reference to the centre of the range.
In the two's complement system, the mapping of real numbers onto the finite range of a binary word is modified.
Instead of the mapping of
Figure 2.37
(
a) in which only positive numbers are mapped, in (b) the upper half of the
pure binary number range has been redefined to represent negative quantities. In two's complement, the range
represented by the circle of numbers does not start at zero, but starts on the diametrically opposite side of the
circle such that zero is now in the centre of the number range. All numbers clockwise from zero are positive and
have the MSB reset. All numbers anticlockwise from zero are negative and have the MSB set. 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.
