Hexadecimal to Binary Conversion — Step by Step Guide with Reference Table

Introduction

Hexadecimal to binary conversion is one of the simplest and most frequently used operations in programming and digital electronics. Since hex is essentially shorthand for binary, converting between them requires no arithmetic — just a lookup table. If you can memorize 16 mappings, you can instantly decode any hex value into binary.

🔧 Convert instantly: Hex to Binary Converter — expand any hex number to binary with step-by-step nibble breakdown.

Why Convert Hex to Binary?

Programmers and engineers constantly encounter hexadecimal in:

• Memory dumps and debuggers (e.g., 0xDEADBEEF)
• CSS color codes (#FF5733)
• Network packet analysis
• Machine code and assembly
• Bit manipulation and flag checking

To understand what those hex values mean at the bit level, you convert to binary.

The Nibble Expansion Method

Since 16 = 2⁴, each hexadecimal digit maps to exactly 4 binary bits (called a nibble). Conversion is a simple one-to-one expansion:

1. Take each hex digit individually (left to right)
2. Replace it with its 4-bit binary equivalent from the table below
3. Concatenate all nibbles — that’s your binary result

Complete Hex to Binary Reference Table

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

Worked Examples

Example 1: Single Digit — A₁₆

A → 1010

Result: 1010 (4 bits, decimal 10)

Example 2: Two Digits — FF₁₆

F → 1111, F → 1111

Result: 11111111 (8 bits = 1 byte = decimal 255)

Example 3: Four Digits — 1A3F₁₆

1 → 0001, A → 1010, 3 → 0011, F → 1111

Result: 0001101000111111 (16 bits)

Drop leading zeros if not needed for fixed-width: 1101000111111

Example 4: CSS Color — #4A7BFF

4 → 0100, A → 1010, 7 → 0111, B → 1011, F → 1111, F → 1111

Binary RGB: R=01001010, G=01111011, B=11111111

Hex to Binary vs Binary to Hex

Direction	Method	Example
Hex → Binary	Expand each digit to 4 bits	F → 1111
Binary → Hex	Group 4 bits from right, convert each	1111 → F

Both are mechanical lookups — no division or multiplication needed.

Common Mistakes

1. Using wrong number of bits — Always use exactly 4 bits per hex digit (even for small values: hex 1 = 0001, not 1)
2. Forgetting leading zeros in nibbles — Hex 3 is 0011, not 11
3. Mixing up A-F values — A=10=1010, not A=1 (it’s not a decimal digit)
4. Processing digits in wrong order — Work left to right for hex-to-binary
5. Confusing with octal — Octal groups 3 bits, hex groups 4 bits

Frequently Asked Questions

How do I convert hex to binary?

Replace each hex digit with its 4-bit binary equivalent using the lookup table. Hex F = 1111, hex A = 1010, etc. Concatenate all 4-bit groups.

What is hex A in binary?

A = decimal 10 = binary 1010. Remember: A is the first hex digit that uses a letter.

How many binary bits does one hex digit represent?

Exactly 4 bits (one nibble). Two hex digits = 8 bits (one byte). Eight hex digits = 32 bits.

Can I convert hex to binary without a table?

Yes — convert the hex digit to decimal (0-15), then convert that decimal to 4-bit binary using the division method. But memorizing the 16 mappings is much faster.

What is 0xFF in binary?

0xFF = FF hex = 1111 1111 binary = 255 decimal. This is the maximum unsigned value for one byte.

Related Calculators

• Hex to Binary Converter
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