Hex to Decimal Converter

Hex to Decimal Converter: Convert Base 16 to Base 10

Convert hexadecimal numbers to decimal instantly with our free hex to decimal converter. Whether you're debugging code, working with memory addresses, analyzing color codes, or learning number systems, this tool provides fast and accurate base 16 to base 10 conversion.

Enter any hexadecimal value (with or without 0x prefix, using digits 0-9 and letters A-F) to see the decimal equivalent. Perfect for programmers, students, and anyone working with hex values.

What Is Hexadecimal?

Hexadecimal (often abbreviated as "hex") is the base 16 number system. It uses 16 distinct symbols to represent values, making it more compact than binary and well-suited for representing computer data.

Hexadecimal Digits

Hex uses:

• 0-9: Represent values 0 through 9 (same as decimal)
• A-F: Represent values 10 through 15

Why Hexadecimal Matters

Compact representation:

• 1 hex digit = 4 binary bits (a "nibble")
• 2 hex digits = 8 bits (1 byte)
• Much shorter than binary for the same value

Examples:

• Binary: 11111111 (8 digits)
• Hex: FF (2 digits)
• Decimal: 255 (3 digits)
• All represent the same value

Perfect alignment with binary:

• Each hex digit corresponds to exactly 4 bits
• Easy conversion between hex and binary
• Natural fit for computer architecture

Common in computing:

• Memory addresses (0x1A2F)
• Color codes (#FF0000)
• Binary file data
• MAC addresses
• Error codes
• Assembly language

Hexadecimal vs Decimal

Decimal (Base 10):

• Uses 10 digits (0-9)
• Each position is a power of 10
• Human-friendly, everyday counting system

Hexadecimal (Base 16):

• Uses 16 symbols (0-9, A-F)
• Each position is a power of 16
• Computer-friendly, compact representation

Example: The number 255

• Decimal: 255 (2x100 + 5x10 + 5x1)
• Hex: FF (15x16 + 15x1)
• Binary: 11111111 (128+64+32+16+8+4+2+1)

How to Convert Hex to Decimal (Step-by-Step)

Converting hexadecimal to decimal uses the positional notation method with powers of 16.

The Method

For each hex digit:

1. Find its decimal value (0-9 stay the same, A=10, B=11... F=15)
2. Multiply by 16 raised to its position (counting from right, starting at 0)
3. Sum all the results

Formula: Decimal = (d0 x 160) + (d1 x 161) + (d2 x 162) + ...

Where d0 is the rightmost digit, d1 is the next digit to the left, etc.

Place Values (Powers of 16)

Example 1: Convert FF to Decimal

Hex value: FF

Step-by-step:

Sum: 240 + 15 = 255

Verification: FF in hex = 255 in decimal

Example 2: Convert 1A3 to Decimal

Hex value: 1A3

Step-by-step:

Sum: 256 + 160 + 3 = 419

Verification: 1A3 in hex = 419 in decimal

Example 3: Convert FACE to Decimal

Hex value: FACE

Step-by-step:

Sum: 61,440 + 2,560 + 192 + 14 = 64,206

Verification: FACE in hex = 64,206 in decimal

Example 4: Convert 10 to Decimal

Hex value: 10

Step-by-step:

Sum: 16 + 0 = 16

Note: 10 in hex equals 16 in decimal, not 10!

Quick Mental Calculation Tips

Single hex digit: Just use the lookup table

• A = 10, B = 11, C = 12, D = 13, E = 14, F = 15

Two hex digits (most common):

• First digit x 16 + second digit
• Example: 2F = (2 x 16) + 15 = 32 + 15 = 47

Powers of 16 to memorize:

• 160 = 1
• 161 = 16
• 162 = 256
• 163 = 4,096
• 164 = 65,536

Hex Digit Value Chart (0-F)

Quick reference for hexadecimal digit values:

Complete Hex-to-Decimal Mapping

Common Two-Digit Hex Values

Larger Common Values

Common Use Cases

Understanding where hex-to-decimal conversion is used helps contextualize its importance.

Memory Addresses and Debugging

Memory dumps:

• Computer memory displayed in hexadecimal
• Each byte shown as two hex digits
• Example: 0x1A2F3C4D represents a memory location

Debugging output:

• Error codes often in hex
• Memory addresses in hex
• Register contents in hex
• Stack traces show hex addresses

Example:

• Address: 0x7FFFFFFF
• Decimal: 2,147,483,647 (max 32-bit signed integer)

Color Codes (Web and Graphics)

HTML/CSS hex colors:

• Format: #RRGGBB (Red, Green, Blue)
• Each component: 00-FF (0-255 in decimal)
• Total: 16,777,216 possible colors

Examples:

• #FF0000: Red (255, 0, 0)
• #00FF00: Green (0, 255, 0)
• #0000FF: Blue (0, 0, 255)
• #FFFFFF: White (255, 255, 255)
• #000000: Black (0, 0, 0)

Converting hex color to RGB decimal:

• #FF5733 -> R:255, G:87, B:51

File Formats and Binary Data

File headers:

• File types identified by hex signatures
• Example: PNG file starts with 89 50 4E 47 (hex)

Checksums and hashes:

• MD5, SHA-256 output in hex
• Example: MD5 hash = 5D41402ABC4B2A76B9719D911017C592

Binary file analysis:

• Hex editors display file contents
• Each byte as two hex digits
• Easier to read than binary

Network and Hardware Identifiers

MAC addresses:

• 48-bit hardware addresses
• Format: 00:1A:2B:3C:4D:5E (hex)
• Converted to decimal for some calculations

IPv6 addresses:

• Written in hexadecimal notation
• Example: 2001:0DB8:85A3:0000:0000:8A2E:0370:7334

Port numbers and protocols:

• Sometimes expressed in hex
• Example: Port 80 (0x50 in hex)

Assembly Language and Low-Level Programming

Machine code:

• Instruction opcodes in hex
• Example: 0xB8 = MOV instruction

Register values:

• CPU registers displayed in hex
• Flags and status registers in hex

Bitwise operations:

• Masks and flags often in hex
• Example: 0xFF00 masks upper byte

Character Encoding

ASCII values:

• Character codes in hex
• Example: 'A' = 0x41 = 65 decimal

Unicode code points:

• U+XXXX notation (hex)
• Example: U+00A9 = (copyright symbol)

URL encoding:

• Special characters as %XX (hex)
• Example: %20 = space (32 decimal)

Developer Examples

Programming languages provide built-in functions for hex to decimal conversion.

JavaScript

Using parseInt() with radix 16:

// Convert hex string to decimal
let decimal = parseInt("FF", 16);
console.log(decimal);  // Output: 255

// More examples
console.log(parseInt("1A3", 16));    // 419
console.log(parseInt("FACE", 16));   // 64206
console.log(parseInt("10", 16));     // 16

// Case insensitive
console.log(parseInt("ff", 16));     // 255
console.log(parseInt("Ff", 16));     // 255

With 0x prefix:

// 0x prefix automatically recognized
let decimal1 = parseInt("0xFF", 16);     // 255
let decimal2 = parseInt("0x1A3", 16);    // 419

// Or use Number() for 0x notation
let decimal3 = Number("0xFF");           // 255
let decimal4 = 0xFF;                     // 255 (literal)

Validation and error handling:

// Check for valid hex
function hexToDecimal(hex) {
    // Remove 0x prefix if present
    hex = hex.replace(/^0x/i, '');
    
    // Validate hex string
    if (!/^[0-9A-Fa-f]+$/.test(hex)) {
        return "Invalid hex input";
    }
    
    return parseInt(hex, 16);
}

console.log(hexToDecimal("FF"));      // 255
console.log(hexToDecimal("0xFF"));    // 255
console.log(hexToDecimal("XYZ"));     // Invalid hex input

Important note: Always specify radix 16 in parseInt() to avoid unexpected behavior with leading zeros.

Python

Using int() with base 16:

# Convert hex string to decimal
decimal = int("FF", 16)
print(decimal)  # Output: 255

# More examples
print(int("1A3", 16))    # 419
print(int("FACE", 16))   # 64206
print(int("10", 16))     # 16

# Case insensitive
print(int("ff", 16))     # 255
print(int("Ff", 16))     # 255

With 0x prefix:

# Using base 0 for auto-detection
decimal1 = int("0xFF", 0)      # 255
decimal2 = int("0x1A3", 0)     # 419

# Or specify base 16 explicitly
decimal3 = int("0xFF", 16)     # 255

# Hex literal in code
decimal4 = 0xFF                # 255

Validation example:

def hex_to_decimal(hex_str):
    """Convert hex string to decimal with validation."""
    # Remove 0x prefix if present
    hex_str = hex_str.replace("0x", "").replace("0X", "")
    
    try:
        return int(hex_str, 16)
    except ValueError:
        return "Invalid hex input"

print(hex_to_decimal("FF"))       # 255
print(hex_to_decimal("0xFF"))     # 255
print(hex_to_decimal("XYZ"))      # Invalid hex input

Underscores in Python 3.6+:

# Python allows underscores for readability
decimal = int("FF_FF_FF_FF", 16)   # 4,294,967,295
print(decimal)

# Also works with 0x
decimal = int("0xFF_FF", 16)       # 65,535

Other Languages

C/C++:

// Using strtol or sscanf
long decimal = strtol("FF", NULL, 16);  // 255

// Or sscanf
int decimal;
sscanf("FF", "%x", &decimal);  // 255

Java:

// Integer.parseInt() with radix
int decimal = Integer.parseInt("FF", 16);  // 255

// Or Integer.decode() for 0x
int decimal2 = Integer.decode("0xFF");     // 255

Ruby:

# to_i with base 16
decimal = "FF".to_i(16)  # 255

# Or hex literal
decimal = 0xFF           # 255

Understanding the 0x Prefix

The 0x prefix is a common notation indicating that a number is in hexadecimal format.

What 0x Means

Origin: Convention from C programming language

• 0x = "hexadecimal" indicator
• Distinguishes hex from decimal numbers
• Prevents ambiguity in code and documentation

Examples:

• 0xFF = 255 decimal (hexadecimal)
• FF = could be ambiguous
• 255 = decimal (no prefix)

Why 0x Is Used

Clarity in programming:

let a = 100;      // Decimal 100
let b = 0x100;    // Hex 100 = Decimal 256

Without the prefix, "100" could mean either decimal 100 or hex 100 (256 decimal). The 0x prefix eliminates confusion.

Other base prefixes:

• 0x or 0X: Hexadecimal (base 16)
• 0b or 0B: Binary (base 2)
• 0o or 0O: Octal (base 8)

Case insensitive: Both 0x and 0X are valid

• 0xFF = 0XFF = 0Xff = 0xff (all equal to 255)

When to Use 0x

Include 0x when:

• Writing hex values in code
• Documenting memory addresses
• Communicating hex values unambiguously
• Following programming conventions

Omit 0x when:

• Context is clearly hexadecimal (like color codes #FF0000)
• Using dedicated hex notation (subscript 16)
• Tool explicitly expects hex without prefix

Most converters: Accept both formats (with and without 0x)

Hex to Binary Conversion

Hexadecimal and binary have a perfect relationship, making conversion between them straightforward.

The 4-Bit Relationship

Each hex digit = exactly 4 binary bits (called a "nibble")

Converting Hex to Binary

Method: Convert each hex digit to its 4-bit binary equivalent

Example 1: F3 (hex) to binary

• F = 1111
• 3 = 0011
• Result: 11110011

Example 2: 1A (hex) to binary

• 1 = 0001
• A = 1010
• Result: 00011010

Example 3: FACE (hex) to binary

• F = 1111
• A = 1010
• C = 1100
• E = 1110
• Result: 1111101011001110

Why Hex Is Used for Binary

Compactness:

• 8-bit binary: 11111111
• 2-digit hex: FF
• Same value, much shorter

Readability:

• Easier to remember FF than 11111111
• Less prone to counting errors
• Natural grouping (each hex digit = 1 nibble)

Byte alignment:

• 1 byte = 8 bits = 2 hex digits
• Perfect alignment for computer memory

Troubleshooting Common Issues

"Invalid input" or "Not a valid hex number"

Problem: Entered characters that aren't valid hexadecimal digits.

Valid hex characters: 0-9, A-F (case insensitive)

Invalid characters:

• Letters G-Z (not hex digits)
• Special symbols (@, #, $, etc.)
• Spaces or punctuation (in some tools)

Example:

• Valid: FF, 1A3, DEAD, BEEF
• Invalid: GHI, XX, 123G, ZZ

Solution:

• Check your input for non-hex characters
• Remember: A-F only, not G-Z
• Remove spaces or special characters

"Input has 0x prefix but tool doesn't accept it"

Problem: Some tools require pure hex without the 0x prefix.

Examples:

• With prefix: 0xFF
• Without prefix: FF
• Both represent 255 decimal

Solution:

• Remove the 0x prefix if tool doesn't accept it
• Check tool documentation
• Most modern tools accept both formats

Note: Our converter accepts both formats (with and without 0x).

"Different result from another calculator"

Possible causes:

Signed vs unsigned interpretation:

• Unsigned: FF = 255
• Signed (8-bit two's complement): FF = -1
• Same hex, different meaning

Bit width assumptions:

• 8-bit: FF = 255 (or -1 signed)
• 16-bit: 00FF = 255, FF00 = 65,280
• Context matters for interpretation

Byte order (endianness):

• Big-endian: 0x1234 = 4,660
• Little-endian: bytes reversed in memory
• Usually not an issue for simple conversions

Solution:

• Verify both tools use same interpretation (unsigned vs signed)
• Check bit width assumptions
• For basic hex-to-decimal, unsigned interpretation is standard

"Case sensitivity issue"

Problem: Wondering if hex is case-sensitive.

Answer: Hexadecimal is not case-sensitive

• FF = ff = Ff = fF (all equal 255)
• FACE = face = FaCe (all equal 64,206)

Convention:

• Uppercase more common in documentation
• Lowercase common in some programming contexts
• Both are equally valid

Solution: Use whichever case you prefer. Tools accept both.

"My hex has spaces or dashes"

Problem: Hex value formatted with separators (e.g., FF-AA-00 or FF AA 00)

Common in:

• MAC addresses: 00:1A:2B:3C:4D:5E
• Color codes: FF AA 00
• Memory dumps: FF AA BB CC

Solution:

• Remove spaces, colons, dashes before converting
• FF-AA-00 -> FFAA00 -> 16755200 decimal
• Or convert each segment separately

"Large number precision"

Problem: Very large hex values may lose precision in some tools or languages.

JavaScript safe integer limit:

• Max: 0xFFFFFFFFFFFFF (253-1)
• Beyond this, use BigInt

Example:

// Loses precision
parseInt("FFFFFFFFFFFFF0", 16);  // Incorrect

// Use BigInt
BigInt("0xFFFFFFFFFFFFFF0");     // Correct

Solution: For very large hex values, use appropriate data types or tools that support arbitrary precision.

Frequently Asked Questions

1. How do I convert hexadecimal to decimal manually?

To convert hex to decimal manually, use the positional notation method:

Steps:

1. Write down the hex number
2. Number positions from right to left, starting at 0
3. Convert each hex digit to its decimal value (A=10, B=11, C=12, D=13, E=14, F=15)
4. Multiply each decimal value by 16 raised to its position
5. Add all results together

Example: Convert 2F to decimal

Step-by-step:

• Position 1: 2 (decimal) x 161 = 2 x 16 = 32
• Position 0: F (=15 decimal) x 160 = 15 x 1 = 15
• Sum: 32 + 15 = 47

Example: Convert 1A3 to decimal

• Position 2: 1 x 162 = 1 x 256 = 256
• Position 1: A (=10) x 161 = 10 x 16 = 160
• Position 0: 3 x 160 = 3 x 1 = 3
• Sum: 256 + 160 + 3 = 419

Quick method for 2-digit hex:

• First digit x 16 + second digit
• Example: 2F = (2 x 16) + 15 = 47

Use this converter: For instant results without manual calculation!

2. What does 0x mean in a hex number?

0x is a prefix that indicates a number is written in hexadecimal (base 16) notation.

Origin: From C programming language convention

• Prevents ambiguity between hex and decimal
• Standard notation in most programming languages
• Case insensitive (0x = 0X)

Examples:

• 0xFF = 255 decimal (hexadecimal)
• 0x10 = 16 decimal (not 10!)
• 0xFACE = 64,206 decimal

Without the prefix: Could be ambiguous

• Is "100" decimal or hexadecimal?
• 0x100 clearly means hex 100 (256 decimal)
• 100 means decimal 100

Other prefixes:

• 0x: Hexadecimal (base 16)
• 0b: Binary (base 2)
• 0o: Octal (base 8)

In conversion tools: The 0x prefix is optional

• Most tools accept both 0xFF and FF
• Both convert to 255 decimal

When to use 0x:

• In programming code
• Documentation and technical writing
• When clarity is needed
• Following language conventions

3. What are A-F in hexadecimal?

A through F are hex digits representing the decimal values 10 through 15.

Since hexadecimal is base 16 (needs 16 distinct symbols), it uses:

• 0-9: Same as decimal (values 0-9)
• A-F: Extended symbols (values 10-15)

Complete mapping:

Why letters?:

• Decimal uses 0-9 (10 symbols)
• Hex needs 16 symbols
• Letters A-F provide the extra 6 symbols
• Allows single-character representation of values 10-15

Case insensitive:

• A = a (both represent 10)
• F = f (both represent 15)
• FACE = face (both represent 64,206)

In practice:

• FF = 15 x 16 + 15 = 240 + 15 = 255
• BAD = 11 x 256 + 10 x 16 + 13 = 2,989
• CAFE = 12 x 4,096 + 10 x 256 + 15 x 16 + 14 = 51,966

Memory aid: A=10, B=11, C=12, D=13, E=14, F=15 (alphabetical continues from 10)

4. Is hexadecimal case-sensitive?

No, hexadecimal is not case-sensitive. Uppercase and lowercase letters represent the same values.

Examples of equivalent hex values:

• FF = ff = Ff = fF (all equal 255)
• CAFE = cafe = Cafe = CaFe (all equal 51,966)
• A1B2 = a1b2 = A1b2 (all equal 41,394)

Why both cases exist:

Uppercase (A-F):

• More common in documentation
• Traditional in printed materials
• Easier to distinguish from digits in some fonts
• Convention in hardware documentation

Lowercase (a-f):

• Common in programming
• Some languages prefer lowercase (CSS colors)
• Easier to type (no shift key needed)

Mixed case:

• Perfectly valid
• Not common in practice
• Tools accept it without issue

Language/tool conventions:

• C/C++: Both accepted, uppercase common
• Java: Both accepted
• Python: Both accepted
• JavaScript: Both accepted
• CSS colors: Usually lowercase (#ff0000)
• Memory dumps: Often uppercase

Best practice: Choose one case and be consistent within a project, but don't worry about case when reading hex values.

5. How many bits is one hex digit?

One hexadecimal digit represents exactly 4 bits (also called a "nibble").

Why 4 bits?:

• Hex is base 16
• 16 = 24
• 4 bits can represent 16 different values (24 = 16)
• Perfect alignment

Single hex digit range:

• Minimum: 0 (binary 0000)
• Maximum: F (binary 1111)
• Total: 16 values (0-15)

Bit patterns for each hex digit:

Multiple hex digits:

• 1 hex digit = 4 bits (nibble)
• 2 hex digits = 8 bits (byte)
• 4 hex digits = 16 bits (word on many systems)
• 8 hex digits = 32 bits (double word)

Examples:

• F = 1111 (4 bits)
• FF = 11111111 (8 bits, 1 byte)
• FFFF = 1111111111111111 (16 bits)
• FFFFFFFF = 32 ones (32 bits)

Practical significance:

• Easy conversion between hex and binary
• Natural alignment with computer architecture
• Compact representation of binary data
• Each byte = exactly 2 hex digits

This is why hex is so popular: Perfect 4-to-1 ratio with binary makes it ideal for representing computer data.

6. Why is hex used so often in computing?

Hexadecimal is ubiquitous in computing for several practical reasons:

1. Compact representation of binary:

• 8-bit binary: 11111111 (hard to read)
• Hex equivalent: FF (much shorter)
• Same information, far more concise

2. Perfect alignment with binary:

• 1 hex digit = exactly 4 bits
• 2 hex digits = exactly 1 byte
• No ambiguity, perfect conversion

3. Easier for humans to read than binary:

• FF is easier to remember than 11111111
• Less prone to counting errors
• Still shows the binary structure

4. Memory addresses:

• RAM addresses in hex (0x1A2F3C)
• Much shorter than binary equivalents
• Natural fit for CPU architecture

5. File and data representation:

• File headers and signatures in hex
• Hex dumps of binary files
• Network packet analysis
• Debugging binary data

6. Color codes:

• Web colors: #RRGGBB format
• Each component 00-FF (0-255)
• Example: #FF0000 = red

7. Low-level programming:

• Assembly language uses hex
• Machine code opcodes in hex
• Register values in hex
• Bitwise operations with hex masks

8. Hardware identifiers:

• MAC addresses
• Serial numbers
• Product IDs
• Error codes

9. Byte boundaries:

• Computer memory organized in bytes
• 1 byte = 2 hex digits exactly
• Natural representation of byte values

Comparison with decimal:

• Decimal: 0-255 (3 digits, variable length)
• Hex: 00-FF (always 2 digits, consistent)
• Hex shows byte boundaries clearly

Bottom line: Hex provides the perfect balance between human readability and computer-friendly representation.

7. Does this converter support negative/signed hex (two's complement)?

Standard hex-to-decimal conversion interprets hex values as unsigned integers (positive only).

Unsigned interpretation (typical):

• FF = 255 (positive)
• FFFF = 65,535 (positive)
• FFFFFFFF = 4,294,967,295 (positive)

Signed interpretation would require:

• Specified bit width (8-bit, 16-bit, 32-bit, etc.)
• Two's complement format
• Different results for same hex value

Example: FF in different contexts

• Unsigned 8-bit: FF = 255
• Signed 8-bit (two's complement): FF = -1
• Same hex, different meaning!

When signed interpretation matters:

• Low-level programming
• Working with CPU registers
• Signed integer operations
• Specific binary file formats

Most general-purpose converters: Use unsigned interpretation

• Simpler and more intuitive
• Covers the common use case
• Matches typical hex usage

For signed values:

• Specify bit width
• Use specialized tools or programming functions
• Understand two's complement representation

Example signed conversion (8-bit):

# Unsigned
int("FF", 16)  # 255

# Signed (manual conversion)
val = int("FF", 16)
if val >= 128:  # Check if negative in 8-bit signed
    val = val - 256
# val = -1

8. What's the maximum hex length this tool supports?

Maximum length depends on the implementation and underlying number system.

Typical limits:

JavaScript-based tools:

• Safe integer range: -(253-1) to (253-1)
• Max hex: 0x1FFFFFFFFFFFFF (13 hex digits)
• Beyond this: precision issues
• Solution: Use BigInt for larger values

Python-based tools:

• Arbitrary precision integers
• No practical limit
• Can handle very large hex values
• Limited only by available memory

Common practical limits:

• 8-bit: 2 hex digits (00-FF)
• 16-bit: 4 hex digits (0000-FFFF)
• 32-bit: 8 hex digits (00000000-FFFFFFFF)
• 64-bit: 16 hex digits

Most web-based converters: Support at least 32-bit (8 hex digits)

• Covers typical use cases
• Memory addresses, colors, checksums
• Sufficient for most applications

For very large hex values:

• Use programming languages with BigInt support
• Specialized mathematical tools
• Command-line utilities (bc, Python)

Example JavaScript precision issue:

// Safe
parseInt("FFFFFFFFFFFFF", 16);   // Works

// Unsafe (>53 bits)
parseInt("1FFFFFFFFFFFFF0", 16);  // Precision lost

// Solution: BigInt
BigInt("0x1FFFFFFFFFFFFF0");     // Correct

9. How do I convert decimal back to hex?

To convert decimal to hexadecimal, use the division by 16 method (reverse of hex-to-decimal).

Manual method:

1. Divide decimal number by 16
2. Record quotient and remainder
3. Convert remainder to hex digit (10=A, 11=B, 12=C, 13=D, 14=E, 15=F)
4. Repeat with quotient until quotient is 0
5. Read hex digits from bottom to top

Example: Convert 255 to hex

Read bottom to top: FF

Example: Convert 419 to hex

Read bottom to top: 1A3

Programming shortcuts:

JavaScript:

let hex = (255).toString(16);  // "ff"
let hex2 = (255).toString(16).toUpperCase();  // "FF"

Python:

hex_val = hex(255)  # "0xff"
hex_val = hex(255)[2:]  # "ff" (remove 0x)
hex_val = format(255, 'X')  # "FF" (uppercase)

Use our Decimal to Hex Converter for instant results!

10. How do I convert hex to binary (and why is it 4 bits per digit)?

Hex to binary conversion is straightforward because each hex digit corresponds to exactly 4 bits.

Why 4 bits per hex digit?:

• Hex is base 16
• 16 = 24
• Each hex digit represents 4 binary bits
• Perfect mathematical alignment

Conversion method:

1. Convert each hex digit to its 4-bit binary equivalent
2. Concatenate all the binary groups
3. Remove leading zeros if desired

Hex-to-Binary table:

Example 1: Convert F3 to binary

• F = 1111
• 3 = 0011
• Result: 11110011

Example 2: Convert 2A to binary

• 2 = 0010
• A = 1010
• Result: 00101010

Example 3: Convert FACE to binary

• F = 1111
• A = 1010
• C = 1100
• E = 1110
• Result: 1111101011001110

Why this relationship is useful:

• Easy mental conversion
• No calculation needed
• Just memorize 16 patterns
• Much simpler than decimal-to-binary

Binary to hex (reverse):

• Group binary digits in sets of 4 from right
• Convert each group to hex digit
• Example: 11010110 -> 1101 0110 -> D6

Use our Hex to Binary Converter for instant results!