Digital Information

1. A thing that just is

The point’s height represents a voltage. The reading on the right reports 0 or 1 and changes only when the point crosses the dashed line. The voltage can change without changing the value we read.

The dashed line marks a threshold in our rule: above counts as 1, at or below counts as 0. The voltage and threshold are measured relative to the same circuit reference. The voltage is a physical quantity; 0 and 1 are the values we use it to represent.

Drag the point anywhere. Away from the line, small movements leave the reading unchanged. Near the line, those same movements can make it switch back and forth. Different physical values can represent the same bit, as long as they stay within the same region.

2. Two ways to read the same point

Switch the reading to Analog to read the same point a different way.

Now the number reports how high the point is, on a scale from 0 to 1: halfway up reads 0.50, a little higher reads 0.52. The display rounds to two decimal places. It illustrates an analog interpretation, where the signal’s magnitude carries information.

Switch back to Digital. The reading reports only which side of the threshold the voltage occupies. A point just above the line and a point at the top of the figure both read 1.

The physical quantity is the same in both views. What changes is the information we take from it: one reading reports its approximate magnitude, while the other reports which of two regions it occupies.

3. Why the line

Analog and Digital read the same point at the same instant. Turn the noise all the way down. The point settles still, and both readings settle with it: one reports its approximate height, the other its side of the line.

Turn the noise up. Noise changes the voltage and can change the analog reading. The digital reading stays the same unless the noise carries the point across the line. Near the line, even a small disturbance can change the bit we read.

The farther the intended voltage is from the line, the more noise it can tolerate before the reading changes. That room for variation is the useful idea behind noise margin. Real circuits specify guaranteed low and high input ranges; the single line here is a simplified decision boundary.

4. When do we read it?

This receiver reads the voltage at regular intervals.

The trace shows the voltage at a point on the wire over time, with now at its right edge. Drag it up or down to see the voltage follow. The rounded edges model a signal that takes time to respond.

The marks below the trace show the clock ticks. At each tick, the receiver records which side of the line the voltage is on. The dot marks that sample on the trace; the digit below records the bit read at that instant.

Set the clock to 8 and drag quickly. Pause the trace to inspect where the samples landed. Sometimes a look lands while the voltage is still changing. Park the voltage near the line and successive samples can disagree, just as the reading flickered in the first figure. Reliable sampling depends on when the receiver looks. In a real circuit, the voltage must stay in the intended valid range for a short interval around that sample.

5. What digital information is

A physical state represents a bit according to a rule. Here, a range of voltages represents 0 and another represents 1. The voltage can vary without changing the represented bit, and it can represent that bit between observations. Sampling records the value at a chosen instant.

That gives us a starting point: physical states can represent discrete values. Further agreements let us use patterns of those values for numbers, letters, images, and messages. That’s where the next entry starts.