Hex ↔ dec ↔ bin ↔ oct with bit width, two's complement and a clickable bit editor.

Bit width & two's complement

The bit width fixes how many bits hold the value, and any operation wraps within it (so on 8 bits, 0xFF + 1 = 0x00). The same bit pattern reads as two different numbers depending on the interpretation:

unsigned = i = 0 \sum n - 1 b_{i} 2^{i} signed = - b_{n - 1} 2^{n - 1} + i = 0 \sum n - 2 b_{i} 2^{i}

That's two's complement: the most-significant bit carries a negative weight, so $0 x F F$ is 255 unsigned but −1 signed on 8 bits. Negating is "invert all bits and add one." Click any bit above to flip it, or use the shift / rotate / bitwise buttons — every view updates live.

Number / Base Converter

Bit width & two's complement