Decimal to Hexadecimal Converter

Decimal to Hexadecimal Calculator is a free online tool prepared by GeekforGeeks that converts the given value of the decimal number into the value of the hexadecimal number. It is a fast and easy-to-use tool that helps students solve various problems.

How 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.

What is Decimal to Hexadecimal Conversion?

Decimal to hexadecimal conversion is the process of converting a decimal number to a hexadecimal number. 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). 

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. 0100 0010

Therefore, Hexadecimal Number =  42₍₁₆₎

Convert Decimal to Hexadecimal

Converting decimal to hexadecimal is simple using a conversion table. Memorize the table for easy conversion of 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

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

Example 4: Convert 0.125 in Hexadcimal

Solution:

To convert a fractional number we multiply the fractional part by 16 and then again multiply the fractional part of the product by 16 till the number becomes zero and then write the result from the first product and not from the last as we do normally.

0.125 ⨯ 16 = 2.0

0 ⨯ 16 = 0

Hence, (.125)₁₀ = 0.2

Practice Questions on Decimal to Hexadecimal Conversion

Q1: 234

Q2: 4573

Q3: 0.1345

Q4: 675434

Q5: 567

FAQs on Decimal to Hexadecimal Conversion

1. How to convert Decimal to Hex?

1. Divide the number by 16.
2. Get the integer quotient for the next iteration.
3. Get the remainder for the hex digit.
4. Repeat the steps until the quotient is equal to 0.

2. In the conversion from Decimal to Hexadecimal, what is the change in bases?

The base from 10 (decimal) changes to 16(hexadecimal).

3. What does 0 mean in hexadecimal?

The Decimal Number 0 is also equal to 0 in Hexadecimal Form.

4. What is Decimal to Hexadecimal Conversion?

Decimal to hex conversion is the process of converting a decimal number with a base of 10 to a hexadecimal number with a base of 16.

5. What is conversion of decimal into hexadecimal?

The conversion of decimal numbers into hexadecimal involves representing decimal values using the base-16 numbering system. In this system, digits from 0 to 9 are represented as usual, and digits from 10 to 15 are represented as A, B, C, D, E, and F, respectively. The process includes dividing the decimal number by 16 repeatedly and noting the remainders to obtain the hexadecimal equivalent. This method allows for easy representation of values in computers, as hexadecimal is commonly used in programming and computing.