In the decimal system there are ten digits -- 0 through 9 -- and each digit represents a power of 10 -- ones, tens, hundred, thousands, etc. In the binary system (base 2) there are only two digits -- 0 and 1 -- and each represents a power of 2 -- ones, two, fours, eights, sixteens, etc.
So the binary number 1101 represents (taking the digits from right to left): 1 one, 0 twos, 1 four, and 1 eight -- in other words, 1101 binary = 13 decimal. Are you with me so far?
Counting in binary goes like this:
DECIMAL BINARY
0 0
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
etc.
Note that, just as decimal powers of ten appear as a one followed by a string of zeroes, in the binary system a one followed by a string of zeroes represents a power of two. For instance, 1000000 = 64 decimal.
In the decimal system, to multiply a number by 10 you append a zero to the right (e.g., 326 x ten = 3260). In the binary system, to multiply a number times 2 you append a zero to the right: 110011 x two = 1100110.
Binary is suited to electronic ciccuitry because with only two digits (0 and 1) you can represent a number with on-off states, usually implemented in hardware with transistors.
Adding two digits together results in: 0+0 = 0; 0+1 = 1+0 = 1; and 1+1 = 10. In the latter case, you can think of it as 1+1=0 with a
carry of 1. Multiplying by 2, which I explained means appending a zero to the end of the number, can be thought of as
shifting the digits one place to the left. Computer circuits are designed around these rules.
I'll try to search the internet for a good tutorial on the subject.
