Hex To Binary Converter
Enter the hexadecimal value to convert to binary or Binary to Hexadecimal.
Hexadecimal:
Hexadecimal is a compact way to represent binary data, commonly used in debugging and low-level programming.
Binary:
Binary is the fundamental number system of all digital computers and electronic devices.
How to Convert Hexadecimal to Binary — Formula:
Replace each hex digit with its 4-bit binary equivalent: 0=0000, 1=0001, ..., 9=1001, A=1010, B=1011, C=1100, D=1101, E=1110, F=1111.
Example: Hex FF → F=1111, F=1111 → Binary 11111111.
Technical Details:
This is a direct digit-by-digit conversion with no arithmetic. Used extensively in: reading memory dumps, analyzing network packets, debugging machine code, and understanding color values.
Hex To Binary Converter:
Each hexadecimal digit converts to exactly 4 binary digits, making this conversion straightforward and commonly used in programming.
Binary ↔ Hex ↔ Octal: Grouping Relationship
Binary → Hex (group by 4 bits):
Binary → Octal (group by 3 bits):
Frequently Asked Questions
How do I convert Hexadecimal to Binary?
Replace each hex digit with its 4-bit binary equivalent: 0=0000, 1=0001, ..., 9=1001, A=1010, B=1011, C=1100, D=1101, E=1110, F=1111.
What is the Hexadecimal number system?
Hexadecimal is a compact way to represent binary data, commonly used in debugging and low-level programming.
What is the Binary number system?
Binary is the fundamental number system of all digital computers and electronic devices.
Where is Hexadecimal to Binary conversion used?
This is a direct digit-by-digit conversion with no arithmetic. Used extensively in: reading memory dumps, analyzing network packets, debugging machine code, and understanding color values.
Can I convert large hexadecimal numbers?
Yes. This converter handles numbers of any practical size. For very large numbers, the conversion is performed using arbitrary-precision arithmetic to ensure accuracy.
How to Convert Hexadecimal to Binary (Base-16 to Base-2)
Converting hex to binary expands each hex digit into its 4-bit binary equivalent. This is essential when working with hardware registers, understanding memory-mapped I/O, or analyzing network packets at the bit level. The conversion is mechanical and lossless — each hex digit maps to exactly one nibble.
- Take each hex digit (0-9, A-F) individually.
- Convert each digit to its 4-bit binary equivalent.
- Concatenate all 4-bit groups left to right.
- Example: 0x3F → 0011 1111₂.
Hex to Binary: Common Values in Computing
Frequently encountered hex values and their binary expansions:
| Input | Output |
|---|---|
| 0x00 | 0000 0000 |
| 0x0F | 0000 1111 |
| 0x55 | 0101 0101 |
| 0x7F | 0111 1111 |
| 0x80 | 1000 0000 |
| 0xAA | 1010 1010 |
| 0xF0 | 1111 0000 |
| 0xFF | 1111 1111 |
Solved Examples: Hex to Binary
Question 1: A hardware status register reads 0xA5. Expand to binary to identify set bits.
Solution:
A₁₆ = 1010₂
5₁₆ = 0101₂
Combined: 10100101₂
Answer: 0xA5 = 10100101₂ — bits 7, 5, 2, and 0 are set (counting from 0).
Question 2: Convert the hex color #4CAF50 (Material Design green) to binary.
Solution:
4₁₆ = 0100, C₁₆ = 1100 → R = 01001100₂ (76)
A₁₆ = 1010, F₁₆ = 1111 → G = 10101111₂ (175)
5₁₆ = 0101, 0₁₆ = 0000 → B = 01010000₂ (80)
Answer: #4CAF50 = 01001100 10101111 01010000₂ — moderate green with balanced R and B channels.
Question 3: A network packet header byte is 0x6E. Convert to binary to decode flags.
Solution:
6₁₆ = 0110₂
E₁₆ = 1110₂
Combined: 01101110₂
Answer: 0x6E = 01101110₂ — in an IPv4 header, this encodes version 4 (0110) and header length 14 (1110 × 4 = 56 bytes).
Practice: Hex to Binary
Try solving these on your own to test your understanding:
- Convert 0x3C to binary. (Answer: 00111100)
- Convert 0xDEAD to binary. (Answer: 1101111010101101)
- Convert 0x7F to binary. (Answer: 01111111)
- Convert 0xC0 to binary. (Answer: 11000000)
- Convert 0x1A to binary. (Answer: 00011010)
Hardware Register Decoding
Embedded engineers read registers in hex and think in binary. A UART status register reading 0x62 (01100010₂) might mean: bit 6 = TX empty (ready to send), bit 5 = TX complete (all sent), bit 1 = overrun error. Each bit is a flag with specific meaning. Without expanding hex to binary, you cannot identify which flags are set. Datasheets list bit positions (0-7) while debuggers show hex values — converting between them is a constant workflow in firmware development.
Network Protocol Analysis with Hex/Binary
Wireshark displays packet bytes in hex. To decode a TCP header, expand each byte to binary: Flags byte 0x12 = 00010010₂ = SYN+ACK (bit 4 = ACK, bit 1 = SYN). The 4-bit header length field in 0x50 (01010000₂) means 5 × 4 = 20 bytes. Protocol analyzers automate this, but understanding hex-to-binary lets you decode packets manually when debugging unusual network behavior.
Key Takeaways
- Each hex digit expands to exactly 4 binary bits.
- Conversion is a lookup: 0→0000, 1→0001, ..., E→1110, F→1111.
- Hardware register values in hex must be expanded to binary for bit-level analysis.
- Network packets displayed in hex require binary expansion for flag decoding.
- The patterns 0x55/0xAA (alternating bits) are used for bus testing and clock recovery.