Editing Logic Circuit

== Logic Circuit ==

# A '''logic circuit''' is the primary control information processor in digital equipment. It is composed of interconnected [[electronic gate|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.''

=== Overview ===

Logic circuits form the foundational building blocks of virtually all modern digital systems, including [[microprocessor|microprocessors]], [[memory (computing)|memory units]], [[arithmetic logic unit|arithmetic logic units (ALUs)]], and programmable controllers. Unlike [[analog circuit|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 gate|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:

{| class="wikitable"
|-
! Gate !! Symbol !! Boolean Expression !! Description
|-
| [[AND gate|AND]] || · || A · B || Output is 1 only when ''all'' inputs are 1
|-
| [[OR gate|OR]] || + || A + B || Output is 1 when ''at least one'' input is 1
|-
| [[NOT gate|NOT]] || ¬ / ′ || Ā || Output is the logical inverse of the input
|-
| [[NAND gate|NAND]] || ↑ || &not;(A · B) || Complement of AND; universal gate
|-
| [[NOR gate|NOR]] || ↓ || &not;(A + B) || Complement of OR; universal gate
|-
| [[XOR gate|XOR]] || ⊕ || A ⊕ B || Output is 1 when inputs ''differ''
|-
| [[XNOR gate|XNOR]] || ⊙ || &not;(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:''' &not;(A · B) = Ā + B̄ ;  &not;(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|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 [[adder (electronics)|adders]], [[multiplexer|multiplexers]], [[decoder|decoders]], and [[comparator|comparators]].

; [[Sequential logic|Sequential Logic Circuits]]
: The output depends on both the current inputs ''and'' the history of past inputs, stored in internal [[flip-flop (electronics)|flip-flops]] or [[latch (electronics)|latches]]. Examples include [[counter (digital)|counters]], [[shift register|shift registers]], and [[finite-state machine|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.
* '''[[Programmable logic device|PLDs]] and [[FPGA|FPGAs]]''' — reconfigurable devices allowing logic circuits to be defined and modified in software.
* '''[[Application-specific integrated circuit|ASICs]]''' — custom-fabricated circuits optimized for a specific application.

=== See Also ===

* [[Boolean algebra]]
* [[Digital electronics]]
* [[Logic gate]]
* [[Combinational logic]]
* [[Sequential logic]]
* [[Integrated circuit]]
* [[Truth table]]
* [[Karnaugh map]]

=== References ===

{{reflist}}

=== Further Reading ===

* Boole, G. (1854). ''An Investigation of the Laws of Thought''. Walton and Maberly.
* Shannon, C. E. (1938). "A Symbolic Analysis of Relay and Switching Circuits". ''Transactions of the American Institute of Electrical Engineers''. '''57''' (12): 713–723.
* Mano, M. M.; Ciletti, M. D. (2013). ''Digital Design''. 5th ed. Pearson Education.
* Wakerly, J. F. (2006). ''Digital Design: Principles and Practices''. 4th ed. Prentice Hall.

[[Category:Digital electronics]]
[[Category:Logic gates]]
[[Category:Boolean algebra]]
[[Category:Computer engineering]]