Decimal to Hexadecimal Conversion Formula

Before learning the decimal to hexadecimal conversion formula, let us recall what is a hexadecimal system and a decimal system. A decimal system is a number system with base 10 and a hexadecimal system is a number system with base 16. Let us learn about decimal to hexadecimal conversion with a few examples in the end.

What Is Decimal to Hexadecimal Conversion Formula?

We can convert this number system to a standard decimal system (base 10) by following some basic mathematical calculations for decimal to hexadecimal conversion. Here are the steps.

• Firstly, divide the given decimal by 16 and keep the remainder aside.
• Now, again divide the quotient by 16.
• Repeat this until the quotient becomes zero.
• Replace 10, 11, 12, 13, 14, 15 by A, B, C, D, E, F in the remainder respectively.
• Arrange all the values of the remainder in reverse order.
• This is your required hexadecimal number.

Decimal to hexadecimal conversion formula of given numbers can be expressed as,

\(X_{10}\) = \(Y _{16}\)

where,

• X = A decimal number
• Y = A hexadecimal number

We can see the applications of the decimal to hexadecimal conversion formula in the following solved examples.

Solved Examples Using Decimal to Hexadecimal Conversion Formula

Example 1: Convert the decimal number 4510 to a hexadecimal number.

Solution: 

To find: Hexadecimal number equivalent to decimal number 4510.

Using decimal to hexadecimal conversion formula,

(4510)\(_{10}\) = \(Y _{16}\)

4510 = 281(16) + 14, Remainder = 14 = E

281 = 17(16) + 9, Remainder = 9

17 = 1(16) + 1, Remainder = 1

1 = 0(16) + 1, Remainder = 1

4510\( _{10}\) = 119E\( _{16}\)

Answer: The decimal number 4510 is equivalent to the hexadecimal number 119E

Example 2: Using the decimal to hexadecimal conversion formula, convert the decimal number 321475 to a hexadecimal number.

Solution: 

To find: Hexadecimal number equivalent to decimal number 321475.

Using decimal to hexadecimal conversion formula,

321475 = 20092(16) + 3, Remainder = 3

20092 = 1255(16) + 12, Remainder = 12 = C

1255 = 78(16) + 7, Remainder = 7

78 = 4(16) + 14, Remainder = 14 = E

4 = 0(16) + 4, Remainder = 4

321475\( _{10}\) = 4E7C3\( _{16}\)

Answer: The decimal number 321475 is equivalent to the hexadecimal number 4E7C3