Binary to Hexadecimal Converter

Embedded systems engineers and firmware developers frequently manage raw data streams where direct binary analysis becomes cumbersome. A binary string expands rapidly in length because it requires eight bits to represent a single byte. This visual expansion leads to alignment errors and difficulty in spotting patterns within memory dumps or register values. Hexadecimal notation compresses this data by a factor of four. A single hex digit represents a nibble or four bits. This compression reduces the cognitive load required to interpret machine code, color codes, or network packet headers. Accuracy remains paramount during this translation. A single flipped bit in a configuration register or a memory address offset results in system failures or segmentation faults. This tool ensures bit-perfect translation by strictly mapping four-bit groups to their corresponding base-16 values.

The conversion relies on grouping bits into sets of four. This set is known as a nibble. Since binary is base-2, a 4-bit number has 42 distinct values (from 0 to 15). Hexadecimal is base-16, which aligns perfectly with this range. The mathematical transformation for a nibble b consisting of bits b₃b₂b₁b₀ is:

If the total bit count of the input stream is not a multiple of four, the system prepends leading zeros. For example, a 6-bit stream 110010 becomes 0011 0010 before conversion to 32₁₆.