440 Chapter 15
well assured of correctly conveying the information requested. At the receiving end the
numbers are plotted on to the chart and, in the simplest approach, they can be simply
joined up with straight lines. The result will be a curve looking very much like the
original.
Let’s look at this analogy a little more closely. We have already recognized that we have
had to agree on the time interval between each measurement and on the meaning of the
units we will use. The optimum choice for this rate is determined by the fastest rate at
which the tidal height changes. If, within the 10-minute interval chosen, the tidal height
could have ebbed and fl owed then we would fi nd that this nuance in the change of tidal
height would not be refl ected in our set of readings. At this stage we would need to
recognize the need to decrease the interval between readings. We will have to agree on
the resolution of the measurement, since, if an arbitrarily fi ne resolution is requested, it
will take a much longer time for all of the information to be conveyed or transmitted. We
will also need to recognize the effect of inaccuracies in marking off the time intervals at
both the transmit or coding end and the receiving end since this is a source of error that
affects each end independently.
In this simple example of digitizing a simple wave shape we have turned over a few ideas.
We note that the method is robust and relatively immune to noise and distortion in the
transmission and we note also that, provided we agree on what the time interval between
readings should represent, small amounts of error in the timing of the reception of each
piece of data will be completely removed when the data are plotted. We also note that
greater resolution requires a longer time and that the choice of time interval affects our
ability to resolve the shape of the curve. All of these concepts have their own special
terms and we will meet them slightly more formally.
In the example just given we used implicitly the usual decimal base for counting. In
the decimal base there are 10 digits (0 through 9). As we count beyond 9 we adopt the
convention that we increment our count of the number of tens by one and recommence
counting in the units column from 0. The process is repeated for the count of hundreds,
thousands, and so on. Each column thus represents the number of powers of 10
(10 101, 100 102, 1000 103, and so on). We are not restricted to using the number
base of 10 for counting. Among the bases in common use these days are base 16 (known
more commonly as the hexadecimal base), base 8 (known as octal), and the simplest of
them all, base 2 (known as binary). Some of these scales have been, and continue to be, in