Hex to Binary Converter

How to Convert Hex to Binary

Converting hexadecimal to binary is one of the most straightforward base conversions in computing. Because hexadecimal is base-16 and binary is base-2, and because 16 is a perfect power of 2 (16 = 2⁴), every single hex digit maps directly to exactly 4 binary bits. No arithmetic is needed — just a simple lookup and substitution.

Step-by-Step Conversion Method

Follow these steps to convert any hexadecimal number to binary by hand:

Step 1: Write down the hex number

Remove any prefix such as 0x or #. For example, 0x2F becomes 2F.

Step 2: Replace each hex digit with its 4-bit binary equivalent

Use the mapping table: 0=0000, 1=0001, 2=0010, 3=0011, 4=0100, 5=0101, 6=0110, 7=0111, 8=1000, 9=1001, A=1010, B=1011, C=1100, D=1101, E=1110, F=1111.

Step 3: Combine all 4-bit groups

Concatenate the binary groups from left to right. The result is the full binary representation.

Why Each Hex Digit Equals 4 Binary Bits

A single hexadecimal digit can represent values from 0 to 15, which is exactly the range of 4 binary bits (2⁴ = 16). This means each hex digit d maps to exactly one 4-bit binary nibble. This perfect power-of-2 relationship is why hexadecimal became the preferred shorthand for binary data in computing, rather than decimal or octal.

Two hex digits represent one byte (8 bits), four hex digits represent a 16-bit word, and eight hex digits represent a 32-bit word. This clean alignment makes hex-to-binary conversion trivially mechanical.

Hex to Binary Conversion Examples

Below are worked examples showing the hex to binary conversion process step by step, from simple single-byte values to multi-byte color codes.

Convert 2F to Binary

• 2 → 0010
• F → 1111
• 2F = 0010 1111 (decimal: 47)

Convert 4FA to Binary

• 4 → 0100
• F → 1111
• A → 1010
• 4FA = 0100 1111 1010 (decimal: 1,274)

Convert FF to Binary

• F → 1111
• F → 1111
• FF = 1111 1111 (decimal: 255 — the maximum value of a single unsigned byte, all 8 bits set to 1)

Convert Color Code #3A7BD5 to Binary

• 3 → 0011
• A → 1010
• 7 → 0111
• B → 1011
• D → 1101
• 5 → 0101
• 3A7BD5 = 0011 1010 0111 1011 1101 0101

The 24-bit result breaks into three bytes: R=00111010 (58), G=01111011 (123), B=11010101 (213).

Hex to Binary Conversion Table (Single Digits 0–F)

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

This table covers all 16 single hex digits. For multi-byte values (00–FF), apply the same 4-bit substitution to each hex digit in sequence. The full 256-entry table (00–FF) is available interactively in the converter above.

Hex to Binary in Programming

Most programming languages provide built-in functions for converting between hexadecimal and binary.

Python

# Convert hex string to binary string
hex_value = "FF"
binary_value = bin(int(hex_value, 16))
print(binary_value)          # '0b11111111'

# Remove '0b' prefix and pad to 8 bits
binary_clean = bin(int(hex_value, 16))[2:].zfill(8)
print(binary_clean)          # '11111111'

# Format with 4-bit groups
hex_value = "3A7BD5"
binary_str = bin(int(hex_value, 16))[2:].zfill(len(hex_value) * 4)
grouped = ' '.join([binary_str[i:i+4] for i in range(0, len(binary_str), 4)])
print(grouped)               # '0011 1010 0111 1011 1101 0101'

JavaScript

// Convert hex string to binary string
const hexValue = "FF";
const binaryValue = parseInt(hexValue, 16).toString(2);
console.log(binaryValue);    // '11111111'

// Pad to 8 bits
const padded = binaryValue.padStart(8, '0');
console.log(padded);         // '11111111'

// For large hex values, use BigInt
const bigHex = "3A7BD5";
const bigBin = BigInt("0x" + bigHex).toString(2).padStart(bigHex.length * 4, '0');
console.log(bigBin);         // '001110100111101111010101'

Java

// Convert hex string to binary string
String hexValue = "FF";
String binaryValue = Integer.toBinaryString(Integer.parseInt(hexValue, 16));
System.out.println(binaryValue);  // "11111111"

// Pad to 8 bits
String padded = String.format("%8s", binaryValue).replace(' ', '0');
System.out.println(padded);       // "11111111"

// For larger values, use Long
String bigHex = "3A7BD5";
String bigBin = Long.toBinaryString(Long.parseLong(bigHex, 16));
System.out.println(bigBin);       // "1110100111101111010101"

Applications

• Digital circuit design and analysis requiring hex to binary conversions
• Computer memory debugging using hex to binary representation
• Binary data manipulation in programming
• Assembly language programming and machine code analysis
• Color code conversions in web development
• Educational purposes for understanding number systems

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