
The hexadecimal number system represents numbers with a base of 16, meaning there are 16 possible values or symbols. The 16 values or symbols are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, and F. The symbols from A to F represent numbers 10 to 15, respectively. To represent any value in hex, it requires 4 bits. They are either suffixed with x or h.
|
Hex digit |
0 |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
|
Binary |
0000 |
0001 |
0010 |
0011 |
0100 |
0101 |
0110 |
0111 |
|
decimal |
0 |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
|
Hex digit |
8 |
9 |
A |
B |
C |
D |
E |
F |
|
Binary |
1000 |
1001 |
1010 |
1011 |
1100 |
1101 |
1110 |
1111 |
|
decimal |
8 |
9 |
10 |
11 |
12 |
13 |
14 |
15 |
Just like the decimal system, the hexadecimal system also has place values. Decimal has the powers of 10, while hexadecimal has the powers of 16.
|
Exponent |
163 |
162 |
161 |
160 |
|
value |
4096 |
256 |
16 |
1 |
|
Exponent |
16-1 |
16-2 |
16-3 |
|
value |
1/16 |
1/256 |
1/4096 |
|
hexadecimal |
Decimal |
|
10 |
16 |
|
100 |
256 |
|
1000 |
4096 |
Example 1 – The number 200 in the hexadecimal number system will be read as what in decimal?
-: = 2x162 + 0x161 + 0x160
= 512
(200)16 = (512)10
Example 2 – The number 200 in the hexadecimal number system will be read as what in binary?
-: 2 – 0010 0 – 0000 0 – 0000
(200)16 = (001000000000)2
(200)16 = (1000000000)2
Sometimes, the binary number system uses hexadecimal in its place. Since 16 is equal to 24, they have a linear relationship between them. It means that one hex can store four binary digits. It shortens the code for the computer, making it easier to understand. It has undoubtedly more uses:
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