Hexadecimal Number System

In a hexadecimal number system, each position is 16 times more important than the previous one. It means in a hexadecimal number, the numeric value is calculated by multiplying each digit of the number by the value of the position in which the digit appears and add the products. It is also called a weighted or positional number system.

Hexadecimal Numbers List

As we know there are 16 Hexadecimal digits. These are digits same as decimal digits till 9, and then letters  in place of numbers 10 to 15:

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 1 1 1 1 1 1
0 1 2 3 4 5

16 Different values can be shown as single hexadecimal instead of normal 10.

Hexadecimal Representation

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).

The Hexadecimal number’s equivalent binary number can be given as:

Hexadecimal Numbers to Binary

Hex Digit Binary
0 0000
1 0001
2 0010
3 0011
4 0100
5 0101
6 0110
7 0111
8 1000
A = 10 1001
B =11 1010
C =12 1011
D = 13 1100
E =14 1110
F = 15 1111

Hexadecimal Number system and Octal Number System are almost similar with the only advantage of hexadecimal number system which makes it easy to convert large binary numbers to a smaller group by making it compact.

Hexadecimal Number System Questions

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.

Test your Knowledge:

What is 5D6(Hexadecimal)?

  • Out of many types of number representation techniques, Hexadecimal number system is one having a value of base 16.
  • So Hexadecimal numbers have 16 symbols or digital values, i.e 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F.
  • A, B, C, D, E, F are single bit representations of 10, 11, 12, 13, 14 and 15 respectively.
  • Addition of either an o prefix or an h prefix indicates Hexadecimal.

A power of 16 is the weight of the position of every digit.

As there are many types of Number systems, Hexadecimal is one of them.

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Practise This Question

In the figure shown, the two lines are parallel to each other. Which of the following options is incorrect?