What Is Binary to Hex Conversion?
Binary (base 2) and hexadecimal (base 16) are two number systems used extensively in computing. Binary is the native language of digital circuits, but long strings of 0s and 1s are hard for humans to read. Hexadecimal solves this by compressing every four binary digits into a single hex digit. Because 16 is exactly 2 to the power of 4, the conversion between binary and hex is direct and lossless, requiring no arithmetic beyond grouping.
This converter works in both directions: binary to hex and hex to binary. It shows the step-by-step 4-bit grouping process so you can see exactly how each group maps to its hex equivalent. For broader base conversions including octal and decimal, use our Number Converter, and for binary arithmetic, try the Binary Calculator.
What This Calculator Does
Choose a conversion direction, enter your value, and see the result instantly. The tool validates input (only 0 and 1 for binary, only 0-9 and A-F for hex) and displays the 4-bit grouping steps that produce the result. A reference table shows all 16 possible 4-bit binary to hex mappings.
- Inputs: A binary or hex value and conversion direction
- Outputs: Converted result, step-by-step grouping, and reference table
How the Conversion Works
Binary to Hexadecimal
1010 1110 => A E => AE
Starting from the right, group the binary digits into sets of four. If the leftmost group has fewer than four digits, pad it with leading zeros. Then map each 4-bit group to its hex equivalent using the standard table: 0000=0, 0001=1, ... 1010=A, 1011=B, 1100=C, 1101=D, 1110=E, 1111=F. For example, 10101110 splits into 1010 and 1110, which map to A and E, giving AE.
Hexadecimal to Binary
Replace each hex digit with its 4-bit binary equivalent. For example, the hex value AE becomes 1010 (for A) followed by 1110 (for E), giving 10101110. No padding or grouping is needed because each hex digit always expands to exactly four binary digits.
How to Use the Calculator
- Select the conversion direction (binary to hex or hex to binary)
- Enter your value in the input field
- The converted result and grouping steps appear instantly
- Use the copy button to copy the result
Example Conversion
Example: Convert the binary number 11010111 to hex. Group from the right: 1101 0111. Map each group: 1101 = D, 0111 = 7. The result is D7. To verify, convert D7 back to binary: D = 1101, 7 = 0111, giving 11010111, which matches the original input.
Why Use Hexadecimal?
Programmers use hexadecimal because it is far more compact than binary while mapping to it perfectly. A 32-bit value takes 32 characters in binary but only 8 in hex. Memory addresses, color codes (like #FF5733), machine code, and byte values are all commonly written in hex. Two hex digits represent exactly one byte, making hex the natural shorthand for binary data. For hex arithmetic operations, use our Hex Calculator.
Common Mistakes to Avoid
- Grouping from the left: Always group binary digits from the right. If you group from the left, the leftmost group may have fewer than four digits and the conversion will be wrong.
- Forgetting to pad: If the binary length is not a multiple of four, pad the left with zeros. For example, 10110 becomes 0001 0110, which is 16 in hex, not 1 0110 mapped incorrectly.
- Using lowercase hex letters: Hex digits A-F can be uppercase or lowercase, but this converter displays uppercase for consistency. Both cases are accepted as input.