Hexadecimal to Binary Converter

Convert hexadecimal numbers (integers and floats) to binary instantly with batch conversion support. Essential tool for programmers, students, and engineers.

When enabled, hex digits are displayed in uppercase. Disable for lowercase display. Conversion is case-insensitive (A-F = a-f).
When enabled, hex values starting with 8-F are interpreted as negative numbers using two's complement. For floating-point numbers, this only applies to the integer part.
Adjust precision for fractional part conversion (higher = more binary bits).
Enter a hexadecimal number (integer or float). Digits 0-9 and A-F (or a-f) allowed. Use '.' for hex point. Prefix with '-' for negative numbers.
A
A.8
F.F
D.6
FF
0.8
1F.3C
80
ABC.DEF
FFFF
-A.8
7F.FF

Batch Conversion: Convert multiple hexadecimal numbers at once. Enter one hex value per line, or separate values with commas, spaces, or tabs. Supports integers and floating-point numbers.

When enabled, hex digits are displayed in uppercase. Conversion is case-insensitive.
When enabled, hex values starting with 8-F are interpreted as negative numbers using two's complement.
Adjust precision for all fractional part conversions in batch mode.
Enter hexadecimal numbers (integers or floats). Digits 0-9 and A-F (case-insensitive) allowed. Each value will be converted separately. Maximum 1000 values.
Simple Hex List
Basic hex values for testing
A A.8 F.F D.6 0.8 FF
Comma-Separated
Values separated by commas
A, A.8, F.F, D.6, 0.8, FF, 80, ABC
Web Color Codes
Common web color hex values
FF0000 00FF00 0000FF FFFF00 FF00FF 00FFFF 000000 FFFFFF 808080 C0C0C0
Converting...

Understanding Binary Numbers and Hexadecimal Conversion

Binary is a base-2 numeral system that uses only two digits: 0 and 1. Hexadecimal to binary conversion is straightforward because each hex digit directly maps to exactly four binary digits (bits).

Conversion Algorithm:

  • Direct Mapping: Each hex digit converts to exactly 4 binary digits
  • Integer Part: Convert each hex digit from left to right
  • Fractional Part: Convert each hex digit after the point from left to right
  • Negative Numbers: Convert absolute value, then add negative sign (or use two's complement for signed hex)
  • Precision: Control how many fractional hex digits to convert (each = 4 binary bits)

Important Notes on Hex to Binary Conversion:

  • Hex to binary conversion is exact (no rounding) for all valid hex numbers
  • Case doesn't matter: A-F and a-f are treated identically
  • Leading and trailing zeros in binary can be removed for clarity
  • Binary results can be very long for large hex numbers (each hex digit = 4 binary digits)
  • Signed hex interpretation (two's complement) changes the meaning of the binary result

Hexadecimal to Binary Conversion Table

Hex Digit Binary (4-bit) Decimal Hex Digit Binary (4-bit) 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

Conversion Examples

1

Hex A.8 to Binary: A = 1010₂, 8 = 1000₂. So A.8₁₆ = 1010.1₂ (trailing zeros removed from fractional part).

2

Hex FF to Binary: F = 1111₂, F = 1111₂. So FF₁₆ = 11111111₂. Decimal equivalent is 255₁₀.

3

Hex D.6 to Binary: D = 1101₂, 6 = 0110₂. So D.6₁₆ = 1101.011₂ (trailing zeros removed).

4

Hex 80 (Signed) to Binary: With signed hex enabled, 80₁₆ = 10000000₂ in 8-bit two's complement, which represents -128₁₀.

5

Hex 1F.3C to Binary: 1 = 0001₂, F = 1111₂, 3 = 0011₂, C = 1100₂. So 1F.3C₁₆ = 00011111.00111100₂ = 11111.001111₂ (leading/trailing zeros removed).

Real-World Applications

  • Memory Dump Analysis: Convert hex memory dumps to binary for bit-level analysis
  • Color Code Processing: Convert hex color codes (e.g., #FF0000) to binary for digital image processing
  • Network Protocol Analysis: Convert hex packet data to binary for protocol decoding
  • Machine Code Disassembly: Convert hex machine instructions to binary for assembly language analysis
  • Digital Logic Design: Convert hex truth tables and state encodings to binary for circuit design
  • Data Encoding/Decoding: Convert Base16 (hex) encoded data back to binary
  • Security Analysis: Convert hex-encoded cryptographic data to binary for analysis

Calculator Features:

  • Converts hex to binary with step-by-step calculations
  • Supports integers, floating-point numbers, and negative numbers
  • Case-sensitive display control (uppercase/lowercase)
  • Signed hex interpretation (two's complement) option
  • Adjustable precision for fractional part conversion
  • Supports batch conversion of multiple hex values
  • Also shows decimal and octal equivalents
  • Export results as CSV or JSON
  • Color-coded hex digits for easy reading
  • Binary bit grouping for readability

Frequently Asked Questions

Hex to binary conversion is a direct mapping process: 1. For each hex digit: Convert it to its 4-bit binary equivalent using the conversion table (0=0000, 1=0001, ..., F=1111) 2. For integer part: Convert each hex digit from left to right 3. For fractional part: Convert each hex digit after the hex point from left to right 4. Combine results: Join all binary digits, placing a binary point between integer and fractional parts This conversion is exact and reversible for all valid hex numbers.

Signed hex interpretation (two's complement) is a way to represent negative numbers in binary/hex: 1. When enabled, hex values where the most significant hex digit is 8-F are interpreted as negative numbers 2. The converter calculates the decimal value using two's complement rules 3. The binary result shows the actual bit pattern (which represents a negative number in two's complement) Use this option when working with signed hex values common in computer systems (e.g., 8-bit signed integers from -128 to 127, where 80₁₆ = -128₁₀). For unsigned hex values (e.g., memory addresses, color codes), keep this option disabled.

The default precision of 4 hex digits is suitable for most applications. This means fractional hex parts will be converted to 4 × 4 = 16 binary bits. For higher accuracy, increase the precision to 8 hex digits (32 binary bits). For quick conversions or when working with standard data sizes (byte, word, etc.), use multiples that match your data size. Higher precision gives more binary bits but increases the length of the result. Remember: each hex digit = 4 binary bits.

Case sensitivity in hex display is purely cosmetic: 1. Conversion: Case doesn't matter for conversion - A-F and a-f are treated identically 2. Display: The case sensitivity toggle controls how hex digits are displayed in results 3. Common conventions: • Uppercase (A-F) is common in assembly language, memory dumps, and older systems • Lowercase (a-f) is common in web development (CSS colors), modern programming, and JSON 4. Input: You can enter hex in either case regardless of the display setting The converter preserves your input case but can display results in your preferred case for consistency.

Common hex formats include: 1. Plain hex: A, FF, 1F.3C (used in programming and mathematics) 2. Hex with prefix: 0xA, 0xFF, 0x1F.3C (common in C, C++, Java, JavaScript) 3. Hex with suffix: A_h, FF_h, 1F.3C_h (common in assembly language) 4. Color codes: #FF0000, #00FF00, #0000FF (web colors with # prefix) 5. Memory addresses: 0x7FFF, 0xFFFF (often with 0x prefix) 6. Unicode code points: U+0041, U+20AC (with U+ prefix) This converter accepts plain hex format (with optional - for negative and . for fractional point). For prefixed formats, remove the prefix before conversion.