Steps:
- Divide the decimal number by 16. Treat the
division as an integer division.
- Write down the remainder (in hexadecimal).
- Divide the result again by 16. Treat the division as
an integer division.
- Repeat step 2 and 3 until result is 0.
- The hex value is the digit sequence of the remainders from the
last to first.
Note: a remainder in this topic refers to the left over
value after performing an integer division.
| HEXADECIMAL |
0 |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
A |
B |
C |
D |
E |
F |
| DECIMAL |
0 |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
11 |
12 |
13 |
14 |
15 |
Example 1
Convert the number 1128 DECIMAL to HEXADECIMAL
| NOTES |
DIVISION |
RESULT |
REMAINDER (in
HEXADECIMAL) |
Start by dividing the number by 16.
In this case, 1128 divided by 16 is 70.5. So the
integer division result is 70 (throw out anything after the
decimal point).
The remainder is (70.5 - 70) multiplied with 16; or (0.5
times 16), which is 8.
|
1128 / 16 |
70 |
8 |
Then, divide the result again by 16
(the
number 70 on the DIVISION column comes from the
previous RESULT).
In this case, 70/16=4.375. So the integer division
result is 4 (throw out anything after the decimal point)
The remainder is (0.375 multiplied with 16, which is 6.
|
70 / 16 |
4 |
6 |
| Repeat. Note here that
4/16=0.25. So the integer division result is 0.
The remainder is (0.25-0) multiplied with 16, which is 4.
|
4 / 16 |
0 |
4 |
Stop because the result is already 0 (0
divided by 16 will always be 0)
|
|
|
|
| Well, here is the answer.
These
numbers come from the REMAINDER column values (read from
bottom to top) |
|
|
468 |
Side note: You can get the remainder of a division using the Modulus
or % operator. Ie: 1128%16=8.
Example 2
Convert the number 256 DECIMAL to HEXADECIMAL
| DIVISION |
RESULT |
REMAINDER (in HEX) |
| 256 / 16 |
16 |
0 |
| 16 / 16 |
1 |
0 |
| 1 / 16 |
0 |
1 |
| |
|
|
| ANSWER |
|
100 |
Example 3
Convert the number 921 DECIMAL to HEXADECIMAL
| DIVISION |
RESULT |
REMAINDER (in HEX) |
| 921 / 16 |
57 |
9 |
| 57 / 16 |
3 |
9 |
| 3 / 16 |
0 |
3 |
| |
|
|
| ANSWER |
|
399 |
Example 4
Convert the number 188 DECIMAL to HEXADECIMAL
| DIVISION |
RESULT |
REMAINDER
(in HEX) |
| 188 / 16 |
11 |
C (12 decimal) |
| 11 / 16 |
0 |
B (11 decimal) |
| |
|
|
| ANSWER |
|
BC |
Note that here, the answer would not be 1112, but BC.
Remember to write down the remainder in hex, not decimal.
Example 5
Convert the number 590 DECIMAL to HEXADECIMAL
| DIVISION |
RESULT |
REMAINDER
(HEX) |
| 590 / 16 |
36 |
E (14 decimal) |
| 36 / 16 |
2 |
4 (4 decimal) |
| 2 / 16 |
0 |
2 (2 decimal) |
| |
|
|
| ANSWER |
|
24E |
See also: Converting Hexadecimal to Decimal
|
