binarytohexdecimal

Binary to hexadecimal conversion is the process of converting a binary number, expressed in base 2, into its hexadecimal representation, base 16. In hexadecimal, each digit represents four binary bits, using digits 0-9 and letters A-F. Because of this one-to-four bit correspondence, converting binary to hexadecimal is straightforward and exact for unsigned values.

Method: To convert, pad the binary string on the left with zeros so its length is a multiple of four. Then split into 4-bit groups from left to right. Replace each 4-bit group with the corresponding hex digit: 0000->0, 0001->1, ..., 1111->F. Concatenate the digits. Leading zeros are usually omitted in the final representation, unless the full width is important.

Example: Binary 11010111 becomes D7, since 1101 maps to D and 0111 maps to 7. Another example: binary 10101 becomes 15 in hex, represented as 0x15, since padded as 0001 0101.

Special cases: If the binary value is signed in two's complement, the resulting hex string represents the underlying bit pattern; there is no separate minus sign in hex. The conversion is independent of endianness when viewed as a single number, though byte order matters in larger sequences.

Applications: The technique is widely used in computing, digital electronics, debugging memory dumps, and data encoding, where hex provides a compact, human-readable form aligned with binary boundaries. Many calculators and programming languages offer built-in bin-to-hex conversion.