2. Binary number system

The binary system

When we count with our fingers, we typically use the unitary system: For each finger we hold up, the total increases by 1.

The resolution of how to count to 31 with 5 fingers can be found in the applet below.

Imagine that each card represents a finger: your thumb represents the card with just one dot, your index finger the one with two dots, and so on. If the card is face up, this corresponds to your outstretched finger.

!    Use the cards to count systematically from 1 to 10.


Computers also use precisely this method of counting. We speak of the binary system because it works in a similar way to the decimal system, but uses only two digits instead of ten (Latin bini “two each” or also as a prefix bi- ‘two’ or “double”).

We will find out how we get from our card representation to binary numbers in the next task.

!    Use the “Show binary representation” button to obtain the respective binary number. Use it to convert the following numbers into their binary equivalent! Have you already managed to convert some numbers without using the applet?




Comparison: Binary and decimal system

In the following table, we have compared the decimal system (left) and the binary system (right) for the first 10 numbers.


0 0
1 1
2 10
3 11
4 100
5 101
6 110
7 111
8 1000
9 1001
10 1010