000 010 100 111

OR Gate: $Y = A + B$

NAND Gate: $Y = \overline{A \cdot B}$

NOR Gate: $Y = \overline{A + B}$

XOR Gate (Exclusive OR): $Y = A \oplus B = \overline{A}B + A\overline{B}$

XNOR Gate (Exclusive NOR): $Y = \overline{A \oplus B} = AB + \overline{A}\overline{B}$

Half Adder: Adds two single-bit binary numbers ($A, B$). Produces a Sum ($S$) and a Carry ($C_{out}$).
$S = A \oplus B$

$C_{out} = A \cdot B$
Full Adder: Adds three single-bit binary numbers ($A, B, C_{in}$). Produces a Sum ($S$) and a Carry ($C_{out}$). Used for multi-bit addition.
$S = (A \oplus B) \oplus C_{in}$

$C_{out} = (A \cdot B) + (C_{in} \cdot (A \oplus B))$

Flip-flops are 1-bit memory elements that store binary data. They are edge-triggered sequential logic circuits.

SR Flip-Flop: (Set-Reset)

S R Q$_{n+1}$ Comment

0 0 Q$_n$ No Change

0 1 0 Reset

1 0 1 Set

1 1 Invalid Undefined state
JK Flip-Flop: (J-K) - resolves SR's invalid state. <

J K Q$_{n+1}$ Comment

0 0 Q$_n$ No Change

0 1 0 Reset