In the base 10 number system, the ones place represents how many 1's, the tens place represents how many 10's, the hundreds place represents how many of 10 squared (100), the thousands place is 10 raised to the 3rd power (1000).
In binary, the number system is based on values of 2 instead of values of 10, so the first place represents how many 1's, the second place represents how many 2's and the third place represents how many 4's (2 x 2), the fourth place represents how many 8's (2 x 2 x 2), etc. Computers use this way of representing numbers because, you only need a 0 and 1 to count up to any number. This can be represented electronically, by an on/off switch, where "on" represents 1 and "off" represents 0. Read more about how computers represent data at TurboFuture. For a complete explanation of the binary number system visit mathisfun.com.
Here is the number 32 (base 10) written in binary (base 2), octal (base 8), duodecimal (base 12) and hexadecimal (base 16):
Using the binary number system, the place values are 1's, 2's, 4's, 8's, 16's, 32's etc.
Each time, you are about to reach the number 2, you carry 1 to the next position.
This is how you would count from 1 - 8:
1
10
11
100
101
110
111
1000
Using the octal number system, the place values are 1'2, 8's, 64's and 512's, etc.
Since the octal number system can represent binary data more compactly (3 binary digits or bits) fit in one octal digit, octal was used for data input and output to computers. Humans can read it better than binary. Hexadecimal is even more compact and is used more frequently now.
This is how you count from 1 - 20 in octal:
1, 2, 3, 4, 5, 6, 7
10, 11, 12, 13, 14, 15, 16, 17
20, 21, 22, 23, 24
24 means 2*8 plus 4
Using the duodecimal system, the place values are 1'2, 12's, 144's, 1728's.
There are many reasons you might want to count by 12's. Inches and hours are both measured in 12's. Dividing by 3 would be easier to represent in base 12, since 12 divided by 3 is an even number, but 10 / 3 is a repeating decimal 3.33333. For representing music, there are also 12 half-step tones in an octave.
If you look at the palm of your hand, you can even count to 12 by looking at the three digits on each of your 4 fingers.
You need two extra symbols to count to 12, so ten is frequently represented by T and eleven by E. This is how you count to 32 in duodecimal:
1, 2, 3, 4, 5, 6,
7, 8, 9, T, E,
10, 11, 12, 13, 14, 15, 16,
17, 18, 19, 1T, 1E,
20, 21, 22, 23, 24, 25, 26, 27, 28
28 means 2* 12 plus 8
To learn how to name and pronounce these numbers and learn about a society that promotes the use of duodecimal check out Wikipedia.
Using the hexadecimal system, the place values are 1's, 16's, 256's, 4096's.
The hexadecimal system is used to read and write data from a computer, because it is readable by people, but is also easily converted to binary. One hexadecimal bit represents 4 binary bits, which is half a byte.
Hexadecimal uses 6 additional digits for 10 - 15, which are represented by the letters A, B, C, D, E and F.
This is how you count to 32 in hexadecimal:
1, 2, 3, 4, 5, 6, 7, 8,
9, A, B, C, D, E, F,
10, 11, 12, 13,, 14, 15, 16,
17, 18, 19, 1A, 1B, 1C, 1D, 1E, 1F,
20
20 means 2 * 16