Binary

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
===
 10   (binary '10' equals decimal '2')

When you add 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.

 

The number above is how the computer represents the value of two (10), and four (100). The decimal system has the symbols 0-9, but binary only has 0 and 1. So each column can only have two possible values. 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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