Decimal To Hex Conversion

Decimal to Hex Conversion: In number system, we have learned about binary numbers, decimal numbers, octal numbers and hexadecimal numbers. All these numbers have different bases such as binary has base 2, decimal has base 10, octal has base 8 and hex has base 16. These numbers can be converted into other number systems by following the methods or procedure. Here we are going to convert a decimal number into a hexadecimal number.

Decimal to Hex

The conversion of decimal number to hexadecimal number is a very easy task. It can be done with the help of conversion table. If one memorize this table, he/she can easily convert a decimal number to hexadecimal number. For the decimal numbers from 1 to 15, there is an equivalent hexadecimal number. But how to convert the decimal number if it is more than 15. Then we need to follow different procedure.

If any given number is more than 15, then we have to divide the decimal number by 16 and consider remainder to get the equivalent hexadecimal number. The complete procedure we have explained here step by step. But before learning the steps let us see the table, where for each value of the decimal number from 0 to 15, there is an equivalent hexadecimal number given.

Decimal to Hexadecimal Table

To convert the decimal number to hex, students have to remember the table given below, to solve the problems in a quick way.

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

How to Convert a Decimal number into Hexadecimal number?

To convert a decimal number into hex follow the below-given, steps;

  • First, divide the decimal number by 16, considering the number as an integer.
  • Keep aside the remainder left.
  • Again divide the quotient by 16 and repeat till you get the quotient value equal to zero.
  • Now take the values of the remainder’s left in the reverse order to get the hexadecimal numbers.

Note: Remember, from 0 to 9, the numbers will be counted as same in the decimal system. But from 10 to 15, they are expressed in alphabetically order such as A, B, C, D, E, F and so on.

Let us take an example to understand the steps given above for decimal to hex conversion.

Example: Convert (960)10 into hexadecimal.

Solution: Following the step,

    • First, divide 960 by 16.

960 ÷ 16 = 60 and remainder = 0

    • Again, divide quotient 60 by 16.

60 ÷ 16 = 3 and remainder 12.

    • Again dividing 3 by 16, will leave quotient=0 and remainder = 3.
    • Now taking the remainder in reverse order and substituting the equivalent hexadecimal value for them, we get,

3→3, 12→C and 0→0

Therefore, (960)10 = (3C0)16

This example must have made you understand the conversion method of decimal to hex. Let us solve a few more examples to get a good practice over it.

Decimal to Hex Examples

Problem 1: Convert decimal number 49 into hexadecimal.

Solution: Let us create a table to solve the problem.

Divide by 16 Quotient Remainder Hex Value
49 ÷ 16 3 1 1
3 ÷ 16 0 3 3

Therefore, 4910 = 3116.

Problem 2: Convert 122810 into hex.

Solution:

Divide by 16 Quotient Remainder Hex Value
1228 ÷ 16 76 12 C
76 ÷ 16 4 12 C
4 ÷ 16 0 4 4

Therefore, 122810 = 4CC16

Problem 3: Convert 60010 into hexadecimal number.

Solution:

Divide by 16 Quotient Remainder Hex Value
600 ÷ 16 37 8 8
37 ÷ 16 2 5 5
2 ÷ 16 0 2 2

Therefore, 60010 = 25816

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