Binary ↔ Hexadecimal Converter
Convert between binary (base 2) and hexadecimal (base 16) instantly
Hexadecimal (hex) is used extensively in computing — from memory addresses and colour codes (like #FF5733) to assembly language and debugging. Binary is the language of computers. This converter helps you switch between both systems instantly.
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How It Works
The Binary-Hex Formula
How to convert between binary and hexadecimal
Formula
Hex = 4-bit binary chunks converted | Binary = each hex digit to 4-bit binary
Variables
Grouping Rule
Every hexadecimal digit represents exactly 4 binary bits (a nibble). This is why hex is so useful — it compresses long binary strings into readable form.
Hexadecimal Digits
Hex uses 0-9 for values 0-9 and A-F for values 10-15. A = 10, B = 11, C = 12, D = 13, E = 14, F = 15.
Binary to Hex Conversion
Group binary digits into sets of 4 (from the right), convert each chunk to its hex equivalent. Add leading zeros to the leftmost group if needed to make 4 bits.
Note: Hexadecimal is the preferred human-readable representation of binary because it is 4× more compact. 8 bits (one byte) is exactly two hex digits: FF = 255, 00 = 0, perfectly mapping to colour values, memory addresses, and network protocols.
Step-by-Step Example
Converting binary 11011010 to hexadecimal
Write the binary number
Binary: 1101 1010
Split into groups of 4 bits from the right
First group: 1101 | Second group: 1010
Convert first group 1101 to hex
1101 binary = 8+4+0+1 = 13 decimal = D in hex
Convert second group 1010 to hex
1010 binary = 8+0+2+0 = 10 decimal = A in hex
Combine results
Binary 11011010 = Hex DA
Reference Guide
| unit | value | note |
|---|---|---|
| Binary 0000 | Hex 0 | 4 bits → 1 hex digit |
| Binary 0001 | Hex 1 | 1 decimal |
| Binary 0010 | Hex 2 | 2 decimal |
| Binary 0011 | Hex 3 | 3 decimal |
| Binary 0100 | Hex 4 | 4 decimal |
| Binary 0101 | Hex 5 | 5 decimal |
| Binary 0110 | Hex 6 | 6 decimal |
| Binary 0111 | Hex 7 | 7 decimal |
| Binary 1000 | Hex 8 | 8 decimal |
| Binary 1001 | Hex 9 | 9 decimal |
| Binary 1010 | Hex A | 10 decimal |
| Binary 1011 | Hex B | 11 decimal |
| Binary 1100 | Hex C | 12 decimal |
| Binary 1101 | Hex D | 13 decimal |
| Binary 1110 | Hex E | 14 decimal |
| Binary 1111 | Hex F | 15 decimal |
Understanding Hexadecimal
Where hex is used in real computing
Hex codes in web design are six-digit numbers: #RRGGBB where each pair (RR, GG, BB) is a hex value from 00 to FF (0–255 decimal). FF = 255 = maximum intensity. 00 = 0 = minimum intensity.
Best for: Example: #FF0000 is pure red, #00FF00 is pure green, #0000FF is pure blue, #FFFFFF is white, #000000 is black.
Memory addresses in debugging tools, crash dumps, and compiler outputs are almost always displayed in hexadecimal. A memory address like 0x7FFD8A3F2B1C is far more compact than its binary equivalent.
Best for: The '0x' prefix indicates a hexadecimal number in many programming languages. 0xFF = 255 decimal.
Machine code (raw processor instructions) is usually represented in hex in debuggers, disassemblers, and hex editors. This allows programmers to read the actual bytes being executed by the CPU.
Best for: 8086 processor instruction 'mov ax, 1' in hex: B8 01 00. Each byte is a hex value (B8, 01, 00).
MAC addresses (permanent hardware addresses for network devices) are six pairs of hex digits. IPv6 addresses are eight groups of four hex digits, totalling 128 bits.
Best for: MAC address example: 00:1A:2B:3C:4D:5E. IPv6 example: 2001:0db8:85a3:0000:0000:8a2e:0370:7334.
Why Hexadecimal Is Used in Computing
Hexadecimal (base 16) is the standard human-readable representation of binary because it is perfectly aligned with bytes: one byte (8 bits) equals exactly two hex digits (8 ÷ 4 = 2). This makes hex 4× more compact than binary while preserving exact correspondence. Binary: 11111111 (8 characters) Hex: FF (2 characters) The hex digits 0-9 represent their values, while A=10, B=11, C=12, D=13, E=14, F=15. This is easier to read, write, and remember than long strings of binary digits. Hexadecimal is used everywhere in computing: memory addresses in debuggers, colour codes in web design (#FF5733), MAC addresses (00:1A:2B:3C:4D:5E), IPv6 addresses, assembly language, machine code, binary file viewers (hex editors), and data encoding formats. Web colours are particularly intuitive: #RRGGBB where RR = red intensity (00–FF), GG = green (00–FF), BB = blue (00–FF). FF = 255 decimal = maximum intensity. This allows 16.7 million distinct colours. Understanding hex is essential for programmers working with low-level code, web developers, network engineers, and anyone who needs to read memory dumps, register values, or packet captures.
Key Features
💡 Pro Tips
- →Memorise the 16 binary-to-hex pairs: 0000=0, 0001=1, 0010=2, 0011=3, 0100=4, 0101=5, 0110=6, 0111=7, 1000=8, 1001=9, 1010=A, 1011=B, 1100=C, 1101=D, 1110=E, 1111=F
- →In web colour codes, #FF = 255, #00 = 0. #FFFFFF is white, #000000 is black, #FF0000 is red.
- →Many debuggers show memory addresses in hex starting with '0x' (e.g., 0x7FFD8A3F2B1C). Our calculator outputs hex without the prefix, but you can add it when needed.
- →Every byte (8 bits) is exactly two hex digits. This is why hex is so efficient — it aligns perfectly with computer architecture.
- →Use the Quick Examples to learn common patterns: FF = 255, 00 = 0, 3F = 63 (often used in networking), FFFF = 65,535
Common Mistakes
Entering letters beyond A-F in hex input
Hexadecimal only uses digits 0-9 and letters A-F (uppercase or lowercase). Letters G-Z will trigger a validation error. Use our dropdown examples to learn the valid characters.
Confusing hex letters with decimal values
In hex, A=10, B=11, C=12, D=13, E=14, F=15. This is not the same as the decimal number system where A has no meaning. Our converter handles this correctly.
Forgetting that hex is case-insensitive
Our converter accepts both uppercase (A-F) and lowercase (a-f) hex letters. The output is always uppercase for consistency.
Expecting hex to have decimal points
Hex is an integer base. It represents whole numbers only. Decimal points (floating point) are not supported — use our Decimal to Binary converter for fractional numbers.
Research & Citations
All factual claims on this page are sourced from peer-reviewed research
- [1]
IEEE Standard for Floating-Point Arithmetic (2019). IEEE 754-2019.
Standard for floating-point representation, which uses hexadecimal for binary interchange format
This calculator is a reference tool and does not constitute medical advice. For personalised sleep health guidance, consult a qualified healthcare provider.
Last updated: January 10, 2025
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Frequently Asked Questions
How do I convert binary to hexadecimal?
Group binary digits into sets of 4 from the right, then convert each 4-bit group to its hex digit (0-F). For example, binary 11011010 → groups 1101 (D) and 1010 (A) → hex DA.
How do I convert hexadecimal to binary?
Convert each hex digit to its 4-bit binary equivalent and concatenate. For example, hex DA → D = 1101, A = 1010 → binary 11011010.
What is hex used for in programming?
Hex is used almost everywhere low-level: memory addresses, register values, colour codes (#FF5733), MAC addresses, IPv6 addresses, assembly language, machine code, and binary file editors.
What does 0x mean before hex numbers?
In many programming languages (C, C++, Java, Python, JavaScript), the prefix '0x' indicates that the following number is hexadecimal. 0xFF means "hex FF" (decimal 255). Our converter outputs plain hex without the prefix, but you can add it manually.
What is the binary representation of hex FF?
Hex FF = decimal 255 = binary 11111111 (eight 1s). This is one full byte of data — used extensively in web colours, network masks, and binary data representation.