By now you might be wondering: if analog computing is so marvelously efficient, why is almost every electronic system you come across digital? One obvious reason is digital's relative immunity to noise. With only two possible values, 1 and 0, noise and other vagaries of the electronic world are unlikely to alter a signal. What's more, digital systems are robust; they are insensitive to changes in temperature, to noise from their power supplies, and to variations among their main constituent parts—transistors. Digital systems also tend to be relatively easy to program and scale up.

The advantage analog computers have is in how they use their transistors and other electronic components. Whereas digital devices use transistors as simple switches, analog systems recognize that transistors are complicated things with physical properties that you can compute with. The use of a transistor's real physical relationship to current and voltage, essentially all the shades of gray between digital's black and white, should let analog computers calculate with much greater efficiency than digital ones. But there are two important limits.

An analog system beats a digital one in efficiency only if the analog system doesn't have to do very precise calculations or output its answer at a high bandwidth. Precision basically means being able not only to compute 2 + 2 to get 4 but also to calculate 1.9866235 + 2.0133765 to get 4.0000000. For an analog system, precision is related to how a device's performance varies with

temperature fluctuations, power-supply noise, slight differences among individual transistors, and inherent and wholly unavoidable fluctuations in the flow of current and thermal noise.

Analog computing's problem with precision is best illustrated by comparing an analog adder to a digital adder. To sum using an analog device, just add the currents entering a particular part of a circuit. To add 4 to 5, put 4 milliamperes on one line, 5 milliamperes on another, and join the two. But notice that both the inputs and the output would have to be accurate to at least a milliamp to get the right answer.

A digital adder needs more circuitry, and thus more power, to operate, but it does not require such high accuracy. An 8-bit number would be represented by eight wires, each carrying either a digital 1 or 0. The logic circuits that add the numbers need only be precise enough to tell a 1 from a 0. Adding bigger or more precise numbers, say a 16-bit number, in a digital adder means just doubling the number of 1-bit wires leading to a similarly increased set of logic circuits. But such an upgrade is much more difficult when adding with analog signals. In fact, it would involve the circuit's going from milliampere accuracy to less than a microampere of accuracy.

Analog computing's other problem, bandwidth, is caused by that unavoidable buzz, thermal noise. In order to eliminate its effect on, say, the answer to an addition problem, analog computers average the answer to a calculation over a period of time. Trying to compute more quickly means less time for averaging and more chance the answer will be corrupted by thermal noise.

So digital processing certainly has its advantages. It is common today, when working with signals from the real world, to convert the signal immediately into a torrent of digital bits using a fast and highly precise analog-to-digital converter and then to do all the subsequent processing with lots of watt-munching digital computations. The processor then spits out a smaller stream of bits that are meaningful to the computer or other device whose job it is to interpret the signal. For example, a typical 16-bit audio converter in a digital voice recorder might churn out 352 kilobits per second of digital data. After lots of digital processing, the signal might result in just 5 kb/s of useful speech data.

What these numbers demonstrate is the inefficiency of turning analog signals into digital bits and running digital processing algorithms on them. The fewer bits that need to be converted and processed, the better. As we noted earlier, nature's solution is to first process the incoming analog information efficiently with interconnected, special-purpose analog devices—eardrums, cochleas, and sensory cells, for instance—and delay the analog-to-digital conversion until after this processing has reduced the amount of information needing to be digitized. For example, rather than report just the intensity of the light falling on each of millions of cells in your retina, interconnected neurons in your eye use analog processes to calculate where the edges in an image lie and encode that data as spikes of voltage on your optic nerve.