How to read binary numbers
Each light is worth twice its neighbor. To read the number, add up the lights that are on.
Read a number
One light: 0 or 1
A computer keeps everything in switches that have only two states: on or off. Here they are lights. A light that is on is worth 1, a light that is off is worth 0. On its own, one light only counts to 1.
Each place is worth double
With several lights side by side, each one is worth twice the one to its right: 1, 2, 4, 8, and so on. To read the number, add up only the lights that are on.
In the example, the lights of 8, 2 and 1 are on: 8 + 2 + 1 = 11. That is why 1011 in binary is 11 in decimal.
Counting from 0 to 15
To add 1, turn on the rightmost light. If it is already on, turn it off and carry the 1 to the next one, just like 9 + 1 = 10 in decimal. With four lights you can count from 0 to 15.
1 + 1 = 10
That is why, in binary, 1 + 1 = 10: the first light goes off and the second one comes on. The binary 10 is worth 2.
Eight lights: a byte
Eight lights together make a byte. All of them on are worth 128 + 64 + 32 + 16 + 8 + 4 + 2 + 1 = 255, the largest number a byte can hold. See why the maximum is 255.