The decimal numeral system has a base value of 10 (0 to 9) and the hexadecimal has a base value of 16 (0 to 9 and A to F for 10-15).
Steps to use Decimal to Hexadecimal Calculator
We can easily use the decimal to hexadecimal converter by following the steps discussed below,
Step 1: Enter the given value in the decimal input field.
Step 2: Click on the convert button to convert the decimal value into the hexadecimal value.
Step 3: The value shown as the result is the required value in the hexadecimal form.
There are different ways to convert Decimal to Hex numbers. They are as follows :
Converting Numbers with the Integer part
Step 1: Take the decimal number as dividend and 16 as the divisor (hexadecimal number will have 16 as a base)
Step 2: Divide the dividend with the divisor and store the remainder in an array
Step 3: Now divide the quotient obtained from the above step by 16 and store the remainder in the array.
Step 4: Repeat the third step until the number is greater than zero.
Step 5: The final hexadecimal value will be the reverse order of the array.
Example 1: Let’s consider a decimal number 450. We need to convert this decimal number to a hexadecimal number.
Solution:
Given: Decimal number = 450(10)
Step 1: 450/16 gives Q1 = 28 and R1 = 2
Step 2: 28/16 gives Q2 = 1 and R2 = 12 = C
Step 3: 1/16 gives Q3 = 0 and R3 = 1
Step 4: 0/16 gives Q4 = 0 and R4 = 0
Therefore, the hexadecimal value is 01C2(16)
Converting Numbers with Fractional Parts
Step 1: Take the decimal fractional number and multiply it with 16 (hexadecimal number will have 16 as a base)
Step 2: Store the remainder in an array i.e. the integer part
Step 3: Repeat the above two steps until the number is zero.
Step 4: The final hexadecimal value will be the elements of the array.
Example 1: Convert 0.0645(10) to _______(16)
Solution:
Given: Decimal number = 0.0645(10)
Step 1: 0.0645 x 16 = 1.032 and R1 = 1
Step 2: 0.032 x 16 = 0.512 and R2 = 0
Step 3: 0.512 x 16 = 8.192 and R3 = 8
Step 4: 0.192 x 16 = 3.072 and R3 = 3
Step 5: 0.072 x 16 = 1.152 and R3 = 1
The fractional part is still not zero so it continues, now we can take up to 5 remainders
Therefore, the hexadecimal value is 0.10831...(16)
Converting Numbers with Both Integer and Fractional parts
Steps of both the integer part and fractional part are to be followed.
Example 1: Convert 256.00390625(10) to _________(16)
Solution:
Given: Decimal number = 256.00390625(10)
Let's perform the conversion on integer part:
Integer value = 256(10)
Step 1: 256/16 gives Q1 = 16 and R1 = 0
Step 2: 16/16 gives Q2 = 1 and R2 = 0
Step 3: 1/16 gives Q3 = 0 and R3 = 1
Let's perform the conversion on fractional part:
Fractional value = 0.00390625(10)
Step 1: 0.00390625 x 16 = 0.0625 and R1 = 0
Step 2: 0.0625 x 16 = 1.0 and R2 = 1
Step 3: 0.0 x 16 = 0 and R3 = 0
Therefore, the hexadecimal value is 100.010(16)
Indirect Conversion
In this type of conversion, we will convert the decimal number to a binary number or octal number and further convert it to a hexadecimal number by grouping digits.
Example 1: Convert 66(10) to _______(16)
Solution:
Given:Decimal Number = 345(10)
Convert the given decimal number to its binary form:
Binary Number = 1000010(2)
Now, Group 4 binary digits as one group and write its hexadecimal value
i.e. 01000010
Therefore, Hexadecimal Number = 42(16)
Convert Decimal to Hexadecimal
Converting decimal to hexadecimal is simple using a conversion table. Memorize the table for easy conversionof numbers 1 to 15. To convert larger numbers, divide by 16 and use the remainder as the hexadecimal digit. Check the table for values 0 to 15 for reference.
Decimal to Hexadecimal Table
The following table shows the representation of Hexadecimal, decimal and binary values:
| Decimal Digit | Hexadecimal Digit | Binary Form |
|---|---|---|
| 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 |
Also Check
Decimal to Hexadecimal Conversion Solved Examples
Example 1: Convert 20 in decimal to hexadecimal
Solution:
We know that to convert a number from decimal to hexadecimal we need to divide the number by 16 and then successively divide the quotient by 16 until quotient is zero
20 ÷ 16 gives Q1 = 1, R1 = 4
1 ÷ 16 gives Q2 = 0, R2 = 1
Hence, 20 in decimal is equal to 14 in hexadecimal
Example 2: Convert (678)10 to Hexadecimal
Solution:
678 ÷ 16 gives Q1 = 42, R1 = 6
42 ÷ 16 gives Q2 = 2, R2 = 10 = A
2 ÷ 16 gives Q3 = 0, R3 = 2
Hence, (678)10 = 2A6 in Hexadecimal
Example 3: Convert (1429)10 into Hexadecimal
Solution:
1429 ÷ 16 gives Q1 = 89 and R1 = 5
89 ÷ 16 gives Q2 = 5 and R2 = 9
5 ÷ 16 gives Q3 = 0 and R3 = 5
Hence (1429)10 = 595 in Hexadecimal
Some Practise Questions :-
Q1: 234
Q2: 4573
Q3: 0.1345
Q4: 675434
Q5: 567