Boolean Algebra: Fundamental binary logic operations: Conjunction ($A \land B$, AND), Disjunction ($A \lor B$, OR), Negation ($\neg A$, NOT), and Exclusive-OR ($A \oplus B = A\overline{B} + \overline{A}B$).
Universal Gate Completeness: NAND ($\overline{A\cdot B}$) and NOR ($\overline{A+B}$) are functionally complete universal gates capable of synthesizing any arbitrary Boolean function.
De Morgan's Laws: $\overline{A \cdot B} = \overline{A} + \overline{B}$ and $\overline{A + B} = \overline{A} \cdot \overline{B}$.
Operating Instructions: Select gate type and toggle input bit states ($0$ or $1$). Inspect the resulting output signal and dynamic truth table highlight.