Boolean Algebra and Logic Gates

NAND and NOR gates are called universal logic gates because any Boolean function or logic circuit can be implemented using only NAND gates or only NOR gates, without needing any other type of gate (AND, OR, NOT). In other words, the three basic gates (NOT, ...

De-Morgan's Theorems are two fundamental theorems in Boolean algebra: Theorem 1: $$\overline{A + B} = \overline{A} \cdot \overline{B}$$ "The complement of a sum equals the product of the complements." Theorem 2: $$\overline{A \cdot B} = \overline{A} + \over...

- Function: Exclusive-OR, $F = A \oplus B = A\bar{B} + \bar{A}B$ - To prove: $F^D = \bar{F}$ (dual equals complement) --- Dual of a Boolean expression: Interchange AND (·) with OR (+), and interchange 0 with 1. Variables (and their complements) remain uncha...

Exclusive-OR (XOR): $$A \oplus B = A'B + AB'$$ Dual of a Boolean function: Replace every AND (·) with OR (+), every OR (+) with AND (·), every 1 with 0, and every 0 with 1. (Variables and their complements are left unchanged.) Complement of a function: Appl...

--- A universal gate is a logic gate that can be used to implement any Boolean function or any other logic gate (AND, OR, NOT, etc.) without needing any other type of gate. The two universal gates are: - NAND Gate - NOR Gate Because all basic gates can be r...