The Binary numeral system is based on two symbols, 0 and 1. Before we get into binary, we have to shift your thinking a bit from the system you already know called the decimal system. Keep in mind that when we count, we use 'symbols'. Symbols are what we write down on paper to represent some quantity of objects. Those of us who use the Arabic numerals use the symbol '4' to represent a quantity of four ( | | | | ) of something. There are only ten symbols from '0' to '9'.
The binary number system only has two symbols: '0' and '1'.
We decimal-using humans count to 9, and then place a 1 in the next column to the left and change the 9 to 0 when we add one, like this:
1
9
+ 1
===
10
When a computer counts, it uses two symbols: 0 and 1. When the computer runs out of symbols, it has to add one to the column to the left and then keep counting. Because 0 and 1 make a total of two symbols, each column in a binary number is worth 2 of the previous column.
When you add binary one to binary one, you get binary two:
1
1
+ 1
===
10 (binary '10' equals decimal '2')
When a computer adds binary one to binary three, you get four:
11 + 1 === 100 (binary '100' equals decimal '4')
OK, I know, you're twitching because the result of the two addition operations above visually appear to be the same pattern we all know as decimal ten and decimal one hundred, but we're doing binary right now, not decimal.
The examples above is show how the computer represents the value of two (10), and four (100). Binary numbers can only have two possible symbols in each colum, either a 1 or a 0. Once you count to one, you have to move to the next column. Each column represents two of the column to the right of it.
Put another way, it could be looked at in terms of powers of two. Remember that in binary, each column is worth two of the previous column:
| 2^3 | 2^2 | 2^1 | 2^0 |
| eights | fours | twos | ones |
| 1000 | 0100 | 0010 | 0001 |
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