Hexadecimal Numbers

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Hex to Binary Conversion

Like the other number systems, the hexadecimal number system is also vividly used in the field of mathematics, computer science and computer application. The hexadecimal Numbers is also the positional number system having base or radix value 16, the numbers in hexadecimal number system is also known as hex numbers. The hex numbers have base 16 so it follows 16 symbols. The symbols used in hexadecimal numbers are 0 - 9 digits and the alphabets A, B, C, D, E, F.

0 ₁₆ = 0 ₁₀ = 0000₂
1 ₁₆ = 1 ₁₀ = 0001₂
2 ₁₆ = 2 ₁₀ = 0010₂
3 ₁₆ = 3 ₁₀ = 0011₂
4 ₁₆ = 4 ₁₀ = 0100₂
5 ₁₆ = 5 ₁₀ = 0101₂
6 ₁₆ = 6 ₁₀ = 0110₂
7 ₁₆ = 7 ₁₀ = 0111₂
8 ₁₆ = 8 ₁₀ = 1000₂
9 ₁₆ = 9 ₁₀ = 1001₂
A ₁₆ = 11 ₁₀ = 1011₂
B ₁₆ = 12 ₁₀ = 1100₂
C ₁₆ = 13 ₁₀ = 1101₂
D ₁₆ = 14 ₁₀ = 1110₂

Hex to Binary Conversion

The hexadecimal number system can be converted into other number systems like binary number system, decimal number system and octal number system. Examples of the conversion of hexadecimal numbers to other number system are given below:

Example 1:

Convert the hexadecimal number 3AB2 to binary.

3AB2₁₆
= (3 * 16³) + (10 * 16²) + (11 * 16¹) + (2 * 16⁰)
= (3 * 4096) + (10 * 256) + (11 * 16) + (2 * 1)
= 12288 + 2560 + 176 + 2
= 15026₁₀

Example 2:

Convert the hexadecimal number 2F3A to binary.

2₁₆ = 0010₂
F₁₆ = 1111₂
3₁₆ = 0011₂
A₁₆ = 1010₂
2F3A₁₆= 0010111100111010₂

Hex to Binary Conversion

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