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The hexadecimal numeral system, or commonly known just as Hex, is a numeral system made up of of 16 symbols (base 16). It uses the common symbols in the decimal numeral system ( 0 through 9 ) and includes six extra symbols. These symbols are characters taken from the English alphabet: A, B, C, D, E and F. The hexidecimal system replaced the Octal numeral system for much of the work done on computers. The most commonly used form of binary is the byte. This is 8 binary digits (bits). Hexadecimal only needs two digits to show the information in one byte of data. As computers become more advanced, they tend to use larger groups of bits but they use multiples of 8 (16, 24, 32, 64, etc). Hexadecimal makes it easier to write these large binary numbers. Hexadecimal numbers are writen with a "h" after the number. For example 63h means 63 hexadecimal.
[change] Hexadecimal values
Hexidecimal is similar to the octal numeral system (base 8) because each can be easily compared to the Binary numeral system. Hexidecimal use a four bit binary coding. This means that each digit in hexidecimal is the same as four digits in binary. Octal uses a three bit binary system.
| Hex |
Binary |
Octal |
Decimal |
| 0 |
0 |
0 |
0 |
| 1 |
1 |
1 |
1 |
| 2 |
10 |
2 |
2 |
| 3 |
11 |
3 |
3 |
| 4 |
100 |
4 |
4 |
| 5 |
101 |
5 |
5 |
| 6 |
110 |
6 |
6 |
| 7 |
111 |
7 |
7 |
|
| Hex |
Binary |
Octal |
Decimal |
| 8 |
1000 |
10 |
8 |
| 9 |
1001 |
11 |
9 |
| A |
1010 |
12 |
10 |
| B |
1011 |
13 |
11 |
| C |
1100 |
14 |
12 |
| D |
1101 |
15 |
13 |
| E |
1110 |
16 |
14 |
| F |
1111 |
17 |
15 |
|
| Hex |
Binary |
Octal |
Decimal |
| 10 |
1 0000 |
20 |
16 |
| 11 |
1 0001 |
21 |
17 |
| 24 |
10 0100 |
44 |
36 |
| 5E |
101 1110 |
136 |
94 |
| 100 |
1 0000 0000 |
400 |
256 |
| 5C2 |
101 1100 0010 |
2702 |
1472 |
| 1000 |
1 0000 0000 0000 |
10000 |
4096 |
| FACE |
1111 1010 1100 1110 |
175326 |
64206 |
|
[change] Conversion
[change] Binary to Hexadecimal
Changing a number from binary to hex uses a grouping method. The binary number is separated into groups of four digits starting from the right. These groups are then converted to hexadecimal digits as shown in the chart above for the hexidecimal numbers 0 through F. To change from hexidecimal, the reverse is done. The hex digits are each changed to binary and the grouping is usually removed.
| Binary |
groupings |
Hex |
| 01100101 |
|
|
0110 |
0101 |
65 |
| 010010110110 |
|
0100 |
1011 |
0110 |
4B6 |
| 1101011101011010 |
1101 |
0111 |
0101 |
1010 |
E75A |
[change] Hexadecimal and Decimal
In the Decimal system (base 10), each digit in hexadecimal is equal to that digit multiplied by the exponent of 16 that is equal to its location minus one. Because hexidecimal uses extra symbols, it is important to remember the decimal value of each of the symbols: A = 10, B = 11, C = 12, D = 13, E = 14, and F = 15.
| |
Location |
| 6 |
5 |
4 |
3 |
2 |
1 |
| Value |
1048576 (165) |
65536 (164) |
4096 (163) |
256 (162) |
16(161) |
1 (160) |
Example: 3425h to decimal
| |
5Fh to decimal
| Hex |
|
Decimal |
| 5Fh |
= |
( 5 x 16) |
+ |
( 15 x 1 ) |
| = |
90 |
+ |
15 |
| 5Fh |
= |
105 |
|
|
3425h to decimal
| Hex |
|
Decimal |
| 3425h |
= |
( 3 * 4096) |
+ |
( 4 * 256 ) |
+ |
( 2 x 16) |
+ |
( 5 x 1 ) |
| = |
12288 |
+ |
1024 |
+ |
32 |
+ |
5 |
| 3425h |
= |
13349 |
|
