About

Binary (base-2) is the native language of digital hardware. Hexadecimal (base-16) compresses every 4 binary digits into a single hex digit, reducing transcription errors by a factor of four. Manual conversion is error-prone: a single misread bit in a 32-bit address flips the hex result entirely, which can corrupt memory maps, MAC addresses, or color codes. This tool validates input, pads to the nearest nibble boundary, and maps each 4-bit group to its hex equivalent. It assumes unsigned, big-endian bit ordering. For signed integers or IEEE 754 floats, interpret the raw hex output according to the relevant standard.

Formulas

Each group of 4 binary digits (a nibble) maps to exactly one hexadecimal digit. The binary string is first left-padded with zeros so its length is a multiple of 4.

H = map(b₃b₂b₁b₀) = b₃ × 8 + b₂ × 4 + b₁ × 2 + b₀ × 1

Where H is the resulting hex digit (0 - F), and b₃ through b₀ are individual bit values (0 or 1). The full hex output is the concatenation of all nibble mappings from most-significant to least-significant.

Reference Data

Binary Nibble	Decimal	Hex
0000	0	0
0001	1	1
0010	2	2
0011	3	3
0100	4	4
0101	5	5
0110	6	6
0111	7	7
1000	8	8
1001	9	9
1010	10	A
1011	11	B
1100	12	C
1101	13	D
1110	14	E
1111	15	F

Frequently Asked Questions

Hexadecimal digits map one-to-one with 4-bit groups (nibbles). If your binary string length is not a multiple of 4, leading zeros are added to complete the most-significant nibble. This does not change the numeric value - for example, 110 becomes 0110, which correctly maps to hex 6.

This tool performs unsigned conversion. For two's complement interpretation, check if the most-significant bit is 1 (negative). If so, the hex output represents the raw bit pattern. To find the magnitude, invert all bits and add 1, then convert. For example, 11111100 converts to hex FC. Inverting gives 00000011, adding 1 gives 00000100 = decimal 4, so the signed value is −4.

Yes. The converter strips all whitespace and newlines before processing. You can enter "0100 1000 0110 0101" or "01001000 01100101" - both produce the same hex output "4865". This makes it easy to paste binary dumps from debuggers or datasheets.

The converter accepts up to 10,000 binary characters (excluding whitespace). This corresponds to 2,500 hex digits or 1,250 bytes - sufficient for most register dumps, MAC addresses, IPv6 addresses, and small binary payloads. JavaScript handles this entirely in-memory with no performance concern.

Hexadecimal groups bits in fours; octal groups in threes. Both are power-of-2 bases, making conversion from binary a direct mapping without arithmetic division. For octal, you would pad to a multiple of 3 instead of 4. This tool specifically targets base-16 output because hex is the dominant notation in programming, networking, and hardware documentation.

The "0x" prefix is a notation convention used in C, JavaScript, and Python to denote hexadecimal literals. This tool optionally prepends "0x" to the output for convenience. It is not part of the numeric value itself. When pasting hex output into code, ensure your language expects the prefix.