Hexadecimal
The hexadecimal system has 16 base. It is represented by using 10 decimal digits plus the alphabet letters (A, B, C, D, E and F). This system facilitates the conversion with the binary code. The table that relates decimal, binary and hexadecimal is:
|
Decimal |
Hexadecimal |
Binario |
|
0 |
0 |
0000 |
|
1 |
1 |
0001 |
|
2 |
2 |
0010 |
|
3 |
3 |
0011 |
|
4 |
4 |
0100 |
|
5 |
5 |
0101 |
|
6 |
6 |
0110 |
|
7 |
7 |
0111 |
|
8 |
8 |
1000 |
|
9 |
9 |
1001 |
|
10 |
A |
1010 |
|
11 |
B |
1011 |
|
12 |
C |
1100 |
|
13 |
D |
1101 |
|
14 |
E |
1110 |
|
15 |
F |
1111 |
Example 1: Transform into binary the following number: 27CE,3A
|
2 |
7 |
C |
E |
, |
3 |
A |
|
0010 |
0111 |
1100 |
1110 |
, |
0011 |
1010 |
Example 2: Transform the decimal number 47599 into binary and hexadecimal:
|
|
Dividend |
Remainder |
|
47599:16 |
2974 |
15 (F) |
|
2974:16 |
185 |
14(E) |
|
185:16 |
11 (B) |
9 |
The final result is B9EF
To pass this number to binary, it is easier to start from the hexadecimal number:
|
B |
9 |
E |
F |
|
1011 |
1001 |
1110 |
1111 |
The transformation from the hexadecimal number to decimal is:
B9EF= 11*163+9*162+14*161+15*160=45056+2304+224+15=47599