Numbering Systems (continued...)

Binary (base 2)
Your computer works using the binary numbering system. This is because a computer can only recognize two states, the presence of an electrical charge or the absence of an electrical charge. In other words, on or off.

The binary numbering system is ideal for representing these two states because it consists of only two digits. The digits, from smallest to largest are:
0, 1.

0 represents the absence of an electrical charge or 'off'.
1 represents the presence of an electrical charge or 'on'.
(Now you can understand why the power switch on your computer is labelled as O/1).

Once again, any number can be broken down into columns. Each column is a placeholder. Using the binary numbering system, from right to left, the first column is the 1's column, then the 2's column, then the 4's, then the 8's, then the 16's column, then the 32's column, etc..
Let's look at the number 137 again:

1 X 128 = 128 (1 one hundred twenty-eights)
0 X 64 = 0 (0 sixty-fours)
0 X 32 = 0 (0 thirty-twos)
0 X 16 =0 (0 sixteens)
1 X 8 = 8 (1 eights)
0 X 4 = 0 (0 fours)
0 X 2 = 0 (0 twos)
1 X 1 = 1 (1 ones)

128 + 0 + 0 + 0 + 8 + 0 + 0 + 1 = 137
Thus, the binary number 10001001 is equal to 137 decimal.

A single digit (0 or 1) is called a 'bit' (binary digit).
The table above contains 8 bits. Each column can contain either a 1 or a 0 ( 'cause there is only 2 digits in the binary numbering system). So, as you can see, it takes 8 bits to represent the decimal number 137.

Make sense?
If you don't understand it this far, go back over it until you do, or get some help.

OK, lets try the number 77:

0 X 128 = 0 (0 one hundred twenty-eights)
1 X 64 = 64 (1 sixty-fours)
0 X 32 = 0 (0 thirty-twos)
0 X 16 =0 (0 sixteens)
1 X 8 = 8 (1 eights)
1 X 4 = 4 (1 fours)
0 X 2 = 0 (0 twos)
1 X 1 = 1 (1 ones)

0 + 64 + 0 + 0 + 8 + 4 + 0 + 1 = 77
Thus, the binary number 01001101 is equal to 77 decimal.

Any character that you type (including spaces), and any character you can see on your screen, takes 8 bits for your computer to produce. Eight bits associated together are called a 'byte'. A byte is the real building block of computer information. This can form a single character. A character can be a number, letter, or symbol. The amount of information a device can store is measured in bytes. Because of this, most numbers and sizes reported by the computer are evenly divisible by 8.
Multiple bytes associated together are often called a 'word'.

8 bits = 1 byte
1024 bytes = 1 kilobyte (Kb)
1024 kilobytes = 1 megabyte (Mb) (1,048,576 characters or bytes)
1024 megabytes = 1 gigabyte (Gb)

These numbers are often rounded off for ease of calculation.
You might see 1 megabyte represented as a million bytes (1,000,000 characters), or 1000 kilobytes.

If you understand this far, go on to the next page for hexidecimal.

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