An analogue signal varies continuously and can take any value in its range

1. Plot the potential difference of an analogue signal against time and you get a smooth, unbroken trace that can sit at any height on the axis.
   1. On its way from $0.50V$ to $0.51V$ it passes through every value in between, because no value is forbidden to it.
2. The exact height of the trace at each instant is what carries the information.
3. An analogue trace does not have to look like a wave, since a slow drift, a single sharp spike and a steady rise are all analogue as long as the value is free to be anything.
4. A car speedometer needle sweeping through every speed between $0km/h$ and $60km/h$ is the same idea in mechanical form.

A digital signal has only two values and travels as a stream of pulses

1. Plotted against time, a digital signal is a run of flat-topped pulses instead of a smooth curve.
   1. The trace holds the high level for a set time, drops almost vertically to the low level, stays there, then jumps straight back up.
   2. It spends no useful time between the two levels, and a value halfway between them carries no meaning for the receiver.
2. Because there are only two possibilities, the receiver never has to measure a size, it only has to answer one question about each pulse, on or off.
3. The information is carried by the pattern and timing of the pulses rather than by how tall they are.
4. A light switch flicked on and off in a coded rhythm sends a digital signal, while a dimmer knob turned slowly round sends an analogue one.

A sound can be sent as either an analogue or a digital signal

1. Sound reaches a microphone as a travelling variation in air pressure, and the microphone turns those pressure variations into a varying potential difference.
   1. That potential difference rises and falls in step with the pressure and can take any value, so it is an analogue signal from the moment it is made.
2. Sent in analogue form, the varying potential difference is carried along the cable or radio link with its shape intact and is fed at the far end straight to a loudspeaker, which pushes the air back and forth to remake the sound.
3. To send the same sound digitally, that varying potential difference is first sampled, meaning its value is measured at regular, very closely spaced instants.
   1. Music on a compact disc is sampled $44100$ times every second, so a single sample stands for only about $23\mu s$ of the original sound.
4. Each sample is then coded as a group of on/off pulses, so a number describing the measured height replaces the height itself, and it is these groups of pulses that travel along the fibre or microwave link.
   1. A group of $16$ pulses can label more than $65000$ different levels, which is fine enough that the steps between them cannot be heard.
5. At the receiving end the pulses are read back as numbers and a circuit turns those numbers into a varying potential difference again, which then drives the loudspeaker.
   1. Whichever route the information took, the thing that finally moves the air is a continuously varying signal.
6. The sound itself is neither digital nor analogue, so the choice is only ever about how the information describing it is sent.

Digital pulses push more data along the same link each second

1. Since the receiver only has to tell on from off, each pulse can be made extremely short and still be read correctly.
2. Electronic switching circuits can turn a current on and off thousands of millions of times a second, so a vast number of pulses fit into every second.
3. This gives digital signalling an increased rate of transmission of data, meaning more information arrives each second along the same cable or carrier.
   1. Pulses belonging to separate conversations can also take turns on one link, which is why a single fibre can deliver television channels and a broadband connection at the same time.

A repeater rebuilds a digital signal exactly, and that is what extends its range

1. Every signal, digital or analogue, grows weaker as it travels, because energy is absorbed and scattered on the way, and this weakening is called attenuation.
2. Every signal also picks up noise, meaning unwanted random additions from nearby electrical equipment, from heat in the conductors and from stray radio waves.
3. After a long distance the trace is both smaller and roughened, so something has to be done to it before it can travel any further.
4. A repeater in a digital link makes only one decision about each pulse, whether it is on or off.
   1. Even a badly roughened pulse is still plainly nearer one level than the other, so that decision is almost always right.
5. The repeater then sends out a brand new pulse of full height and clean shape in its place, so the noise is thrown away instead of being passed on.
   1. What leaves the repeater is an exact copy of the pattern that was sent, so a chain of a hundred repeaters still delivers that same pattern.
6. An analogue signal cannot be treated this way, because any value is a legitimate value, so no circuit can tell the wanted variation apart from the noise riding on top of it.
7. All an analogue link can do is amplify, and an amplifier enlarges the noise by exactly the same factor as the signal.
   1. Each amplifier adds fresh noise of its own on top of what is already there, so distortion builds up at every stage and a long analogue line sounds steadily hissier.
8. Digital signalling therefore has an increased range, because the signal can be regenerated accurately stage after stage, while an analogue signal only ever gets worse.

A two-value signal can be processed, stored and copied without loss

1. Because a digital signal is nothing but a pattern of on and off, an electronic circuit can store it, delay it, sort it or check it for errors and still hand back the identical pattern.
2. Copying is exact for the same reason, since reading each value as on or off and writing it down again introduces no error at all.
   1. A sound file copied a thousand times between computers is identical to the first one, whereas a recording copied a thousand times between analogue tapes ends up buried in hiss.