Comparing and combining

Comparing and combining

A sensor that reports a number cannot be used to make a decision on its own — 23 is neither true nor false. An operator turns that number into an answer by comparing it with something.

Blocks reference

<(x) > (50)>

<(x) < (50)>

<<> and <>>

<<> or <>>

Try it: which way round does it go?

Forget the symbols for a moment. A comparison is a question about position on a number line: is x to the left of the other number, or to the right? Left is smaller, right is bigger — and that is the whole of it.

Drag the orange x and the black marker, and change the comparison. The green stretch is every position of x that would make the answer true — so you can see where the answer flips before you get there. Turn not on and watch the green jump to the other side.

• < is true while x sits on the left. Slide x past the marker and it flips.
• > is the same question the other way round — so exactly one of the two is true, unless the markers are on the same spot.
• = is true for one single position out of twenty-one. Try landing on it. That is why a sensor is almost never compared with =: a reading passes straight through the exact number without ever being measured there.
• not flips the answer, whatever it was. not (x < 4) covers everything x < 4 does not — including landing exactly on 4.

Try it: which numbers make it true?

The lab above asks one question at a time: is this x true? A robot never has just one x, though — a sensor reading slides up and down all the time, so what really matters is which stretch of the line makes the condition true. This one draws the whole answer at once.

Drag the circle to move the number you are comparing against, and change the comparison. Everything shaded green is a value of x that would make it true.

Watch the circle, because it carries the part everyone gets wrong:

• Hollow ○ — the boundary is not included. x < 0.2 shades everything left of 0.2 but leaves 0.2 itself out, because 0.2 is not less than 0.2.
• Filled ● — the boundary is included. Choose = and nothing is shaded at all: one single number qualifies.

Now turn not on with x > 2 selected and watch two things happen together. The shading jumps to the other side, and the circle fills in — because “not greater than 2” means 2 or less, and 2 has to be part of it. That pairing is the whole reason a hollow circle is worth drawing.

Why a robot cares. Two conditions that look almost identical — light < 30 and not (light > 30) — differ by exactly one value, the reading of precisely 30. A robot sitting right on its threshold behaves differently under the two, and that is the sort of bug that only shows up occasionally and looks like a broken sensor.

Try it: and, or, not

These three join answers together rather than numbers. The trap is that English is looser than a program: “stop if it is close and the bumper is pressed” sounds like it covers both situations, when it covers neither on its own.

Flip the two conditions and watch the table. There are only four possible situations in total, and and and or differ on exactly two of them.

• and is true on one row out of four. It narrows — the robot acts less often, but more certainly.
• or is true on three rows out of four. It widens — the robot acts more readily.
• The two agree on the top and bottom rows and disagree in the middle. Whenever swapping one for the other seems to make no difference, you have only tried the rows where they agree.

Watch them decide

Two sensors are running below: an Ultrasonic reporting a number, and a Touch Sensor reporting true or false. Watch the comparison turn the number into an answer, and watch and and or disagree.

The comparison is doing one job: it takes a reading that is neither true nor false and, by holding it against a number you chose, produces something a decision can use. The moment the blue fill crosses the black marker is the moment the answer changes.

Choosing the threshold

The number you compare against is a design decision, not a fact. “Close” for a parking sensor might be 15 cm; for a robot arm it might be 3. Pick it by measuring what the sensor actually reads in the situation you care about, then leave a margin.

Combining two conditions

and narrows: both must hold, so the robot acts less often but more certainly — stop only if something is close and the bumper is pressed. or widens: either will do, so the robot acts more readily — stop if something is close or the bumper is pressed.

In the four situations above, and was true in one of them and or in three. That is the practical difference: swapping one for the other does not adjust a robot slightly, it changes how often it reacts at all.