Recording - February 2016 - 70

would have transmitted the signal digitally-the only thing that passes
between the originator and receiver of the message is a stream of numbers.
The digital-to-analog converter only recognizes numbers-the voltage it puts
out is only controlled by what numbers it sees on its input.
Of course, when you send the numbers down the line, that transmission
will pick up a little bit of noise on the way. But because the D/A converter
responds only to numbers, it will ignore the low-level random fluctuations on
the transmission line, and the decoded will not have added noise.
If, instead of transmitting the numbers, you found a way to record them,
then play them back, you could make a digital recording which would be
essentially impervious to the imperfections of the recording medium. The D/A
converter would only respond to the numbers, and the recording medium
wouldn't add any noise to the signal. In theory, you could copy the signal,
then make a copy of the copy, and keep doing that until the cows came
home without picking up an iota of noise; only if the noise was so bad that it
made the numbers unintelligible would it affect the signal. A digital signal is
what engineers call robust: as long as the D/A converter receives
"269...1,209...5,414...1,332" you'll get the same waveform at the output.

deviations; they only pay attention to the
IS/ISN'T information. Since those tiny deviations are what we call noise and distortion, that
means that a system which expresses digital
information in a binary fashion is inherently
good at separating what's wanted (numbers)
from what's not (random fluctuations).
Now it gets tricky. You'll note that it only took
nine bits to encode 269, but 13 bits to encode
5,414. (Count 'em and see.) Nine bits can
encode any number from (decimal) 0 to 511,
but ten bits can encode numbers as high as
1,023 (plus zero) and sixteen bits can encode
up to 65,535 (plus zero). In effect, the number
of bits tells you how thin a slice a digital system
can resolve, and therefore how subtly the system
can differentiate between different levels. (We
call this the bit depth or resolution.) Compact
discs use 16 bits; professional recording systems
nowadays use 24 bits, which can theoretically
encode 16,777,216 levels (including zero).
That's some mighty thin-sliced pastrami.
What happens if the encoder, or analog-todigital converter, gets an input voltage that's
precisely between two levels-say, 268.5
instead of 269? Well, 268 (in a 16-bit system)
would translate 0000000100001100, but
269 translates as 0000000100001101.
Neither is exactly correct, but the system has to
choose one or the other. We say the system is
quantized, meaning it can only express certain
fixed levels. It will choose essentially at random, and randomness, in electronics, usually
means noise. So the noise created by a sampled system is called, reasonably, quantization
noise. Real digital systems use something called

Why is digital recording useful, anyway? To know that,
we need to take a (massively simplified) look at how it works.

3
Bits and pieces
Of course, as I'm sure you know, digital audio doesn't really use numbers
in decimal (base-10) notation, because electronic circuits don't really handle
those very well. If the numbers are translated into binary (base-2) notation,
the circuits are much happier. So 269 translates as 100001101, 5,414 is
expressed as 1010100100110 and 1,332 becomes 10100110100. Each
of those 0s and 1s is a binary digit, abbreviated as bit.
Why is binary useful? Each of the bits can be expressed as something
which is one of two (and only two) alternatives. A transistor can be turned on
or off, a piece of magnetic tape (or hard disk) can have a spot where all of
the oxide particles are oriented in one direction or the opposite, an optical
medium can have a dot or no dot in a particular location, etc. (The late Mike
Seeger used to refer to digital audio as the "yes-or-no method of recording.")
That all-or-nothing character means that digital devices tend to ignore tiny
70

RECORDING February 2016

dither to smooth out the quantization-but
dither goes beyond the First Steps that this
series encompasses. Just think of it as "magic
noise"-a very small random signal that makes
digital systems behave properly at low levels.
The level of quantization noise controls how
much dynamic range the system has. It's controlled by the bit depth, and is equal, in theory,
to 6 dB times the number of bits. So a 16-bit
system has a theoretical dynamic range of 96
dB, whereas a 24-bit system has a theoretical
dynamic range of 144 dB.
As my guru once said, "In theory, there is no
difference between theory and practice. In
practice, there is." So it is with dynamic range
and bit depth; real-world 16-bit systems usually
have actual dynamic ranges of about 92 dB,
while real-world 24-bit systems have real-world
dynamic ranges of somewhere between 110
dB and 120 dB.
The short message of the above paragraphs is
that a digital system translates the voltages it
samples from the original waveform into digital
numbers; systems with more bits can discern
finer distinctions between levels, and are quieter.

Table of Contents for the Digital Edition of Recording - February 2016