Concept 2 - Binary Numbers

Steve > Projects > Computer > Binary Numbers

Computers work with numbers. Whether counting internet packets on the network, or balancing your checkbook, a computer needs to use numbers. The problem: computer's only know 1's and 0's. The solution: binary numbers.

Say we have three wires, it's easy to decide how to represent zero.


Then for number one we could use 001, but what about two? 011 could work, and then 111 for three. With this scheme, to count above 3 we'd need more wires. But there are a few combinations that we haven't used yet, like 101 or 010.

How do we count in decimal? After we hit 9 (or 009) we start over with 010 then up to 019. So every time we get to the bigest digit, we just increase the digit to the left and start over. So with just three spaces we can count all the way to 999.

A wire holds only 1 (on) and 0 (off), so it can't count up to nine, but we'll use the same idea. When we get to the highest digit (1) we'll just increase the next wire to the left, and start over.

               

Now we've counted to three, but still haven't even used third wire. As we can see in the following table with three wires we can count from zero to seven.

 decimal  binary 
0 000
1 001
2 010
3 011
4 100
5 101
6 110
7 111

And so we have a system to count using only ones and zeros. The following table gives a reference on some more numbers.

 decimal  binary 
0  0000  0000 
1 0000  0001
2 0000  0010
3 0000  0011
4 0000  0100
5 0000  0101
6 0000  0110
7 0000  0111
8 0000  1000
9 0000  1001
10 0000  1010
11 0000  1011
12 0000  1100
13 0000  1101
14 0000  1110
15 0000  1111
16 0001  0000
17 0001  0001
18 0001  0010
19 0001  0011
20 0001  0100
21 0001  0101
22 0001  0110
23 0001  0111
24 0001  1000
25 0001  1001
26 0001  1010
27 0001  1011
28 0001  1100
29 0001  1101
30 0001  1110
31 0001  1111
32 0010  0000
. . .. . .
254 1111  1110
255 1111  1111