Why is the present moment called “the digital age”? What does it mean to have digital electronics, as opposed to analog? What’s so useful about digital?

In present-day electronics, the bulk of the calculations and computing are done on digital circuits, hence the “digital age” moniker. To get into what this means, we have to take a look back at the early development of calculating machines that used electronic signals. There are lots of components you can use in an electronic circuit, and with some basic resistors and capacitors you can start to build circuits that add one voltage to another, or perform other simple mathematical calculations. Early electronic calculators were made to mimic physical calculators and controllers that operated using gears or other mechanisms, such as the Antikythera mechanism, astrolabes, or even slide rules. Most physical calculators are analog, meaning that they apply an operation, like addition, to a set of numbers that can be anywhere along a continuous spectrum. Adding 3 to 6 and getting 9 is an analog operation. But it turns out that analog electronics have a reliability problem: any variation in the output, which could be due to changes in the circuit’s environment, degradation in the circuit components, or leaking of current out of the circuit, will be indistinguishable from the actual signal. So if I add 3 volts to 6 volts, but I lose half a volt, I’ll get 8.5 volts and have no way of knowing whether that’s the answer I was supposed to get or not. For some applications, this isn’t an issue if the person using the electronics is able to calibrate the circuit before operation, or if you have some method of double-checking your result. But if you want to build consumer electronics, where the user is not an expert, or electronics that can reliably operate without adjustment somewhere inaccessible, reliability is a huge issue.

But what if, instead of having a continuum of possible values, we instead use a small number of discrete values? This is called digital computation after the digits of the hand, which are frequently used to count the integers from 1 to 10. Digital computing deals in only two states: on and off, also known as true and false, or 0 and 1. It allows us to hide all the messiness of the analog world by assigning on and off to a wide range of voltage values: for example, we could have 0-2V mean off, and 3-5 V mean on. Now we have a very large margin of error in our voltage ranges, so a little leakage or signal degradation will not affect what we read as the circuit output. The graph below shows how an oscillating analog signal would look as a digital signal.

Physically, there are several ways to build a system that can switch between on and off. The first one that gained a foothold in technological use was the vacuum tube, which is somewhat similar to an incandescent light bulb. In a vacuum tube, a filament can be heated to emit electrons, which are collected at an electrode nearby. The electrons are passed through a region of empty vacuum to get from the filament to the electrode, hence the name, and a control grid induces an electric field that can change how much current passes through the vacuum tube. Early computers had to have one of these vacuum tubes for each switch, hence the massive size of the first computers which easily filled a room or several rooms. If you read science fiction from the vacuum tube era, computers play a big role, quite literally since people assumed that any computer that had the power to rival the human brain would have to be large enough to fill huge underground caverns.

The development of silicon as a material for electronics changed everything. Silicon can be turned on or off as a conductor of electrons simply by applying a voltage, and it can be manufactured so that the switch size is much smaller than the smallest vacuum tube. The scale of the smallest features you can make from silicon has been decreasing for decades, which means we are building computational chips with more and more switches in a given area.

But, one tricky thing about moving to digital logic is that the best math for these calculations is not much like our everyday math. Fortunately, a construction for doing digital calculations was developed in the mid-nineteenth century by George Boole. More on that next time!

Very nicely done. Thanks.

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