How to convert decimal numbers into hexadecimal numbers using repeated division by 16?

To convert a decimal number into a hexadecimal number using repeated division by 16, follow these steps:

1. Divide the decimal number by 16.
2. Write down the remainder (which will be a single digit in the range of 0-15) as the least significant digit of the hexadecimal number.
3. Divide the quotient from step 1 by 16.
4. Write down the remainder as the next least significant digit of the hexadecimal number.
5. Repeat steps 3 and 4 until the quotient is 0.
6. Write down the remainders in reverse order to get the hexadecimal number.

For example, let's convert the decimal number 255 into a hexadecimal number:

1. 255 divided by 16 is 15 with a remainder of 15 (F in hexadecimal).
2. Write down F as the least significant digit.
3. 15 divided by 16 is 0 with a remainder of 15 (F in hexadecimal).
4. Write down F as the next least significant digit.
5. The quotient is now 0, so we stop.
6. The hexadecimal representation of 255 is FF.

Therefore, the decimal number 255 is equivalent to the hexadecimal number FF.

Steps for Converting Decimal to Hexadecimal Using Repeated Division:

1. Divide the decimal number by 16. Record the remainder and divide the quotient by 16.

2. Repeat step 1 until the quotient becomes 0.

3. Arrange the remainders in reverse order. The rightmost remainder is the least significant hex digit, and the leftmost remainder is the most significant hex digit.

Example:

Convert decimal number 125 to hexadecimal.

```
125 ÷ 16 = 7 remainder 13 (D)
7 ÷ 16 = 0 remainder 7 (7)
```

Therefore, the hexadecimal equivalent of 125 is D7.

Hexadecimal Values for Decimal Digits:

| Decimal Digit | Hexadecimal Digit |
|---|---|
| 0 | 0 |
| 1 | 1 |
| 2 | 2 |
| 3 | 3 |
| 4 | 4 |
| 5 | 5 |
| 6 | 6 |
| 7 | 7 |
| 8 | 8 |
| 9 | 9 |
| 10 | A |
| 11 | B |
| 12 | C |
| 13 | D |
| 14 | E |
| 15 | F |

Tips:

- If the remainder is greater than 9, use the corresponding hexadecimal digit (A-F).
- If the quotient is 0, stop dividing and continue with the next remainder.
- The hexadecimal number can be written with or without the prefix "0x".