Understand and define the functions of the following basic logic gates: NOT, AND, OR, NAND, NOR and XOR (EOR).
Fundamental Concepts
Logic gates are electronic devices that implement Boolean functions. Each gate has one or more binary inputs and a single binary output. The output is determined by a logical operation applied to the inputs.
Gate Definitions and Symbols
NOT (Inverter) – produces the complement of its single input.
AND – output is true only if all inputs are true.
OR – output is true if any input is true.
NAND – the complement of AND; output is false only when all inputs are true.
NOR – the complement of OR; output is true only when all inputs are false.
XOR (EOR – Exclusive OR) – output is true when an odd number of inputs are true (for two inputs, true when exactly one input is true).
Truth Tables
NOT Gate
Input \$A\$
Output \$\overline{A}\$
0
1
1
0
AND Gate (2‑input)
\$A\$
\$B\$
\$A \cdot B\$
0
0
0
0
1
0
1
0
0
1
1
1
OR Gate (2‑input)
\$A\$
\$B\$
\$A + B\$
0
0
0
0
1
1
1
0
1
1
1
1
NAND Gate (2‑input)
\$A\$
\$B\$
\$\overline{A \cdot B}\$
0
0
1
0
1
1
1
0
1
1
1
0
NOR Gate (2‑input)
\$A\$
\$B\$
\$\overline{A + B}\$
0
0
1
0
1
0
1
0
0
1
1
0
XOR (EOR) Gate (2‑input)
\$A\$
\$B\$
\$A \oplus B\$
0
0
0
0
1
1
1
0
1
1
1
0
Symbolic Representation
Standard symbols used in circuit diagrams are shown below. (In a real diagram, each symbol would be drawn; here we provide a textual description.)
NOT: a triangle pointing to a small circle (inversion bubble).
AND: a flat‑sided shape (D‑shape) with a curved back.
OR: a curved shape resembling a shield.
NAND: AND symbol with an inversion bubble.
NOR: OR symbol with an inversion bubble.
XOR: OR symbol with an additional curved line on the input side.
Suggested diagram: Standard gate symbols for NOT, AND, OR, NAND, NOR, XOR.
Building Complex Circuits
Any Boolean function can be constructed using combinations of the basic gates. Two common approaches are:
Sum‑of‑Products (SOP) – uses AND gates to form product terms, OR gates to sum them, and optionally NOT gates for complemented inputs.
Product‑of‑Sums (POS) – uses OR gates to form sum terms, AND gates to product them, with NOT gates for complemented inputs.
Because NAND and NOR gates are functionally complete, a circuit can be built using only NAND gates or only NOR gates.
Key Points to Remember
NOT inverts a single binary value.
AND requires all inputs true; OR requires at least one true.
NAND and NOR are the inverses of AND and OR respectively.
XOR outputs true when an odd number of inputs are true (for two inputs, exactly one).
Truth tables are essential for verifying gate behaviour.
All Boolean functions can be realised using combinations of these gates.