Notes for Neil Zwillinger's Fifth Grade Class: Jean-Claude Chetrit 2/2/98
First, we will start with some boring stuff about the decimal system, the system everyone uses all the time. It is called decimal because we use 10 different symbols: 1, 2, 3, ... 9 and 0. We say that the decimal system is a positional system because the meaning of these sym You already know that in the number 232, the first 2 stands for 200 because of its position on the left, while the second 2 stands for just 2 because of its position on the right. We use 10 symbols (1, 2, 3, ..., 8, 9 and 0) and their position matters: the decimal system, also called "base 10", is a positional system.
Now, we are going to look at the binary system, also called "base 2". The binary system is a positional system where we are allowed just two symbols, 0 and 1.
|
Decimal |
Binary |
|
1 |
1 |
|
2 |
10 |
|
3 |
11 |
|
4 |
100 |
|
5 |
101 |
|
6 |
110 |
|
7 |
111 |
|
8 |
1000 |
|
9 |
1001 |
|
10 |
1010 |
|
11 |
1011 |
|
12 |
1100 |
|
13 |
1101 |
|
14 |
1110 |
|
15 |
1111 |
|
16 |
10000 |
|
17 |
10001 |
|
18 |
10010 |
|
19 |
10011 |
|
20 |
10100 |
In the decimal system the columns are for ones, tens, 100s, etc…
In the binary system, the columns are for ones, twos, fours, eights, etc…
Let's look at binary number
1011
starting from the left: The first 1 means 8, the 0 means we have no fours, the next 1 means two and the last 1 means 1:
8 + 2 + 1 = 11
Last updated on January 8, 1999
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