Lamps are like numbers
Although we normally refer to a lamp as being On or Off, we
could equally describe it as being
One or Zero or 1 or 0 and they could have the same meaning as
On or Off. They're just words - it's their meaning that's important.
The four 0's at the top of the picture represent the four lamps as being Off. Press the button a few times and note the 'pattern' of 1's and 0's as you press. Note the number just above the button is keeping a count of the number of button-presses you make.
Each pattern of the lamps is representing a different number between 0 and 15.
Note that I've shown that the fourth lamp represents a value of 8 + the value represented by the other lamps. It is said to have a weighting of 8. Similarly, the third light has a weighting of 4, the second a weighting of 2 and the first has a weighting of 1.