Hex to Binary Converter

What Is Hexadecimal?

Hexadecimal is a number system with base 16. It uses digits 0 to 9 and letters A to F. Each hex digit has a value from 0 to 15. This system represents binary data in a shorter, easier form for people to read, write, and study.

What Is Binary System?

Binary is a base 2 number system. It uses only 0 and 1. Each 0 or 1 is a bit. Computers use binary to represent and process digital data, instructions, numbers, and other information. Binary is the basic language of digital systems.

How to Convert Hex to Binary Manually

You can convert hex to binary without a decimal step. Each hexadecimal digit matches four binary bits. This works because hexadecimal uses base 16, while binary uses base 2. Use the conversion table to replace each digit, then join the groups. For example, $2F = 0010\ 1111$. You can keep leading zeros when you need fixed four bit groups. This method works well for students because it uses one simple rule. It also makes each step easy to check against the table.

Formula

$1$ hexadecimal digit $=$ $4$ binary bits.

For a value with $n$ hex digits, the full binary form uses $4n$ bits.

For example, $3$ hex digits use $3 × 4 = 12$ bits.

Step by step Guide

1. Write the hexadecimal number.
2. Split it into individual hex digits.
3. Find the four bit binary value for each digit.
4. Join the binary groups from left to right.
5. Keep leading zeros when you need fixed four bit groups.
6. Check the result by converting it back to hexadecimal.

Practical Example

Take the hexadecimal value $3CF8$. Replace each digit using the table: $3 = 0011$, $C = 1100$, $F = 1111$, and $8 = 1000$.

Join the groups to get $3CF8 = 0011\ 1100\ 1111\ 1000$.

The result contains $16$ bits because the original value has $4$ hex digits.

Hex to Binary conversion table

Note: Each hexadecimal digit maps to four binary bits. Keep the four bit groups together when you need a fixed width result, such as a byte or word.

Hexadecimal to Binary Without Using Decimal

You can convert hexadecimal to binary directly without changing it to decimal first. Match every hex digit with its four bit binary value, then join the groups. For example, $7E = 0111\ 1110$. This direct method is faster and easier for most student exercises.

Implementing Conversion in Code

You can also convert hexadecimal to binary with code. Python and JavaScript include built in methods that make base conversion simple.

Python

In Python, int() reads the hexadecimal value, and bin() returns its binary form. The 0b prefix marks the result as binary.

hex_value = "7E"
binary_value = bin(int(hex_value, 16))
print(binary_value) # 0b1111110

Remove the 0b prefix if you need only the binary digits.

JavaScript

In JavaScript, parseInt() reads the hexadecimal value, while toString(2) changes the number to base 2.

const hexValue = "7E";
const binaryValue = parseInt(hexValue, 16).toString(2);
console.log(binaryValue); // 1111110

Add padding when your task requires four bits for every hexadecimal digit.