Logic Circuit

A logic circuit is the primary control information processor in digital equipment. It is composed of interconnected electronic gates whose collective operation is described by equations drawn from a specialized branch of mathematics known as Boolean algebra (also called logic algebra or switching algebra).

The primary control information processor in digital equipment; made up of electronic gates, and so named because their operation is described by simple equations of specialized logic algebra.
A logic circuit is a fundamental building block of digital systems that processes binary information using interconnected logic gates. These gates (such as AND, OR, NOT, NAND, etc.) are electronic components whose behavior is governed by Boolean algebra, the mathematical framework for manipulating variables that have only two possible states (0 and 1).

Overview

Logic circuits form the foundational building blocks of virtually all modern digital systems, including microprocessors, memory units, arithmetic logic units (ALUs), and programmable controllers. Unlike analog circuits, which process continuously varying signals, logic circuits operate on discrete binary states, conventionally represented as 0 (low/false) and 1 (high/true). The behavior of any logic circuit, regardless of complexity, can be fully described and predicted using the equations of Boolean algebra, first formalized by mathematician George Boole in the mid-nineteenth century and later adapted for electrical engineering by Claude Shannon in his landmark 1937 thesis.

Electronic Gates

The elemental components of a logic circuit are logic gates — discrete electronic switching elements that accept one or more binary inputs and produce a single binary output according to a defined logical function. The fundamental gate types include:

Gate	Symbol	Boolean Expression	Description
AND	·	A · B	Output is 1 only when all inputs are 1
OR	+	A + B	Output is 1 when at least one input is 1
NOT	¬ / ′	Ā	Output is the logical inverse of the input
NAND	↑	¬(A · B)	Complement of AND; universal gate
NOR	↓	¬(A + B)	Complement of OR; universal gate
XOR	⊕	A ⊕ B	Output is 1 when inputs differ
XNOR	⊙	¬(A ⊕ B)	Output is 1 when inputs are equal

Logic Algebra

The operation of logic circuits is governed by logic algebra (Boolean algebra), a formal system in which variables take only the values 0 or 1, and expressions are evaluated using logical operators. Key identities include:

Identity laws: A + 0 = A ; A · 1 = A
Null laws: A + 1 = 1 ; A · 0 = 0
Idempotent laws: A + A = A ; A · A = A
Complement laws: A + Ā = 1 ; A · Ā = 0
De Morgan's theorems: ¬(A · B) = Ā + B̄ ; ¬(A + B) = Ā · B̄

These identities allow engineers to simplify complex circuit expressions, minimize gate count, and optimize performance, a process formally known as logic minimization.

Types of Logic Circuits

Logic circuits are broadly classified into two categories:

Combinational Logic Circuits: The output at any instant depends only on the current combination of inputs. They contain no memory or feedback elements. Examples include adders, multiplexers, decoders, and comparators.
Sequential Logic Circuits: The output depends on both the current inputs and the history of past inputs, stored in internal flip-flops or latches. Examples include counters, shift registers, and finite-state machines.

Implementation Technologies

Modern logic circuits are implemented using a variety of technologies:

Transistor-transistor logic (TTL) — a legacy bipolar transistor family widely used from the 1960s through the 1990s.
CMOS (Complementary Metal-Oxide-Semiconductor) — the dominant technology in contemporary integrated circuits, prized for low power consumption.
PLDs and FPGAs — reconfigurable devices allowing logic circuits to be defined and modified in software.
ASICs — custom-fabricated circuits optimized for a specific application.

Logic Circuit

Logic Circuit

Overview

Electronic Gates

Logic Algebra

Types of Logic Circuits

Implementation Technologies

See Also

Further Reading