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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, that is
(1128/16).
1128 divided by 16 is 70.5. So the
integer division result is 70 (throw out anything after the
decimal point).
Record it on the RESULT column.
The remainder is (70.5 - 70) multiplied with 16; or (0.5
times 16), which is 8.
Record it on the REMAINDER column.
|
1128 / 16 |
70 |
8 |
Then, divide the result again by 16, that is
(70/16).
(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 in programming code). 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 100 DECIMAL to HEXADECIMAL
| DIVISION |
RESULT |
REMAINDER
(HEX) |
| 100 / 16 |
6 |
4 |
| 6 / 16 |
0 |
6 |
| |
|
|
| ANSWER |
|
64 |
Example 6
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
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