Numbering Systems:

As you know, computers use a BINARY numbering system ( 0, 1 ). Every key that you enter is converted into a series of zeros and ones.

The letter H = 00010011    -    The letter E = 00101101     The number 5 = 00110101

* See ASCI chart

Decimal = Base 10 ( the one we know and love )

Octal = Base 8

Binary = Base 2

Hexadecimal = A "shortcut" method of representing binary numbers.

Lets start with converting Base 10 numbers to base 2 (Binary)
 

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

32768

16384

8192

4096

2048

1024

512

256

128

64

32

16

8

4

2

1

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Value

=

11

 

 

 

 

0

0

0

0

1

0

1

1

 

Value 

=

32

 

 

 

 

0

0

1

0

0

0

0

0

 

Value

=

31

 

 

 

 

0

0

0

1

1

1

1

1

 

Value 

=

129

 

 

 

 

1

0

0

0

0

0

0

1

 

Value 

=

1

 

 

 

 

0

0

0

0

0

0

0

1

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

HEXadecimal is used as an efficient way to store many binary numbers.

It takes binary numbers and breaks them into four digit groups. It then uses the numbers 0-9 and A-F

A=10, B=11, C=12, D=13, E=14, F=15

B=30

 

0

0

0

1

1

1

1

0

HEX=1F

 

1

F

 

B= 283

 

1

1

1

1

0

0

1

1

HEX=F3

 

F

3


 

 

The OCTAL system does the same thing using 3 digit groups instead of 4.
 

B=30

 

0

0

0

1

1

1

1

0

Octal=036

0

3

6

 

B= 283

 0

1

1

1

1

0

0

1

1

Octal=363

3

6

3