Hexadecimal to Binary Converter

Hexadecimal Number System

The base of the hexadecimal number system is 16. Hence, there are 16 symbols or digits in this system. The first ten digits are similar to that of decimal number system - 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. The rest six digits are represented by the symbols A, B, C, D, E, and F, representing decimal numbers 10, 11, 12, 13, 14, and 15 respectively. The largest single digit is F (1 less than the base 16). Each digit in hexadecimal number system represents a power of the base (16). This number system is used to represent colors in HTML programming; FF0000 represents Red, 00FF00 represents Green, 0000FF represents Blue, etc.

Binary Number System

Machines use binary number system to perform computations. This number has a base of 2. Hence, there are 2 digits in this system - 0 and 1. Each digit in binary number system represents a power of the base (2).

How to convert Hexadecimal to Binary

Let's understand the conversion by following these steps-

1. Convert each hexadecimal digit to its equivalent decimal value.
2. Convert the decimal values obtained in Step 1 to 4-digit binary.
3. Combine all the binary groups of four digits each into a single binary number.

The steps mentioned above will become clearer when we apply them in an example. Suppose we have a hexadecimal number 4CD that we want to convert into binary number.

Step i) Convert each hexadecimal digit to its equivalent decimal value.

4₁₆ = 4₁₀
C₁₆ = 12₁₀
D₁₆ = 13₁₀

Step ii) Convert the decimal values obtained in Step 1 to 4-digit binary.

4₁₀ = 0100₂
12₁₀ = 1100₂
13₁₀ = 1101₂

Step iii) Combine the binary groups

4CD₁₆ = 010011001101₂

Hexadecimal to Binary Conversion Table

The following table provides a list of few hexadecimal numbers and their corresponding binary numbers-