Hexadecimal Number System

In the hexadecimal number system, the numbers are represented with base 16. It is also pronounced sometimes as ‘hex’. Just like the binary number, octal number and decimal number whose base representation are 2, 8 and 10, respectively, the hexadecimal conversion is also possible which can be represented in a table.

Hexadecimal Numbers List

Decimal Numbers 4-bit Binary Number Hexadecimal Number
0 0000 0
1 0001 1
2 0010 2
3 0011 3
4 0100 4
5 0101 5
6 0110 6
7 0111 7
8 1000 8
9 1001 9
10 1010 A
11 1011 B
12 1100 C
13 1101 D
14 1110 E
15 1111 F

Hexadecimal Number System Conversions

As we know there are 16 digits in hexadecimal numbers, represented from 0 to 9 same like decimals, but after that, it starts with an alphabetical representation of preceding numbers such as A, B, C, D and E. Let us see the conversion of ‘hex’ into other number systems.

Hexadecimal to Decimal Number System Conversion

Here, you will see the representation of a hexadecimal number into decimal form.

Hexadecimal

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

15

Decimal to Hexadecimal Number System Conversion

You have learned how to convert hexadecimal number to decimal number. Now let us find out how we can convert a decimal number in hexadecimal. Follow the below steps;

  • Firstly divide the number by 16.
  • Take the quotient and divide again by 16,
  • The remainder left will produce the hex value.
  • Repeats the steps until the quotient has become 0.

Example: Convert (242)10 into hexadecimal.

Solution: Divide 242 by 16 and repeat the steps, till the quotient is left as 0.

Therefore, (242)10 = (F2)16

Hexadecimal to Octal Number System Conversion

Here, you will see the representation of a hexadecimal number into octal number form.

Hexadecimal

0 1 2 3 4 5 6 7 8 9 A B C D E F
Octal 0 1 2 3 4 5 6 7 10 11 12 13 14 15 16

17

Octal to Hexadecimal Number System Conversion

To convert octal to hex, we have to first convert octal number to decimal and then decimal to hexadecimal. Let us understand it with the help of an example;

Example: Convert(121)8 into hexadecimal.
Solution: First convert 121 into decimal number.

⇒1 × 82 + 2 × 81 + 1 × 80
⇒1 × 64 + 2 × 8 + 1 × 1
⇒64 + 16 + 1
⇒81

(121)8 = 8110
Now converting 8110 into hexadecimal number.

Therefore, 8110 = 5116

Hexadecimal to Binary Number System Conversion

Here, you will see the representation of a hexadecimal number into binary form. As we can use only 4 digits to represent each hexadecimal number, where each group has a distinct value from 0000(for 0) and 1111(for F= 15 =8+4+2+1).

Hexadecimal

0 1 2 3 4 5 6 7 8 9 A B C D E F
Binary 0 1 10 11 100 101 110 111 1000 1001 1010 1011 1100 1101 1110

1111

Binary to Hexadecimal Number System Conversion

Binary to hexadecimal conversion is a simple method to do. You just have to put the values of the binary number to the relevant hexadecimal number.

Example: Convert(11100011)2 to hexadecimal.
Solution: From the table, we can write, 11100011 as E3.

Therefore, (11100011)2 = (E3)16

Hexadecimal Number System Conversion Examples

Example 1: What is 5C6 (Hexadecimal)?

Solution: Step 1: The “5 “ is the “16 x 16” position, so that means 5 x16 x16

Step 2: The ‘C’ (12) is in the “16” position, so that means 12 x 16.

Step 3: The “6” in the “1” position so that means 6.

Answer is : 5C6 = 5 x 16 x 16 + 12 x 16 +6 = (1478 ) in Decimal.

Example 2: What is 3C5 (Hexadecimal)?

Solution: Step 1: The “3 “ is the “16 x 16” position, so that means 3 x16 x16

Step 2: The ‘C’ (12) is in the “16” position, so that means 12 x 16.

Step 3: The “5” in the “1” position so that means 5.

Answer is : 5C6 = 3 x16 x 16 + 12 x 16 +5 = ( 965) in Decimal.

Example 3: What is 7B5 (Hexadecimal)?

Solution: Step 1: The “7 “ is the “16 x 16” position, so that means 7 x16 x16

Step 2: The ‘B’ (11) is in the “11” position, so that means 11 x 16.

Step 3: The 5” in the “1” position so that means 5.

Answer is : 7B5 = 7 x 16 x 16 + 11 x 16 +5 = (1973) in Decimal.

Example 4: What is 2E8 (Hexadecimal)?

Solution: Step 1: The “2 “ is the “16 x 16” position, so that means 2 x16 x16

Step 2: The ‘E’ (14) is in the “16” position, so that means 14 x 16.

Step 3: The “2” in the “1” position so that means 2.

Answer is : 2E8 = 2 x 16 x 16 + 14 x 16 +8 = (744 ) in Decimal.

Example 5: What is 4F8 (Hexadecimal)?

Solution: Step 1: The “4 “ is the “16 x 16” position, so that means 4 x16 x16

Step 2: The ‘F’ (15) is in the “16” position, so that means 15 x 16.

Step 3: The “8” in the “1” position so that means 8.

Answer is : 4F8 = 4 x16 x 16 + 15 x 16 +8 = (1272) in Decimal.