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


=== Electronic Gates ===
=== Electronic Gates ===
 
The elemental components of a logic circuit are [https://en.wikipedia.org/wiki/Logic_gate logic gates] — discrete [https://en.wiktionary.org/wiki/electronic electronic] [https://en.wiktionary.org/wiki/switching switching] elements that accept one or more [https://en.wiktionary.org/wiki/binary binary] inputs and produce a single binary output according to a defined logical [https://en.wiktionary.org/wiki/function function]. The fundamental gate types include:
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"
{| class="wikitable"
|-
|-
! Gate !! Symbol !! Boolean Expression !! Description
! Gate !! Symbol !! Boolean Expression !! Description
|-
|-
| [[AND gate|AND]] || · || A · B || Output is 1 only when ''all'' inputs are 1
| [https://en.wikipedia.org/wiki/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
| [https://en.wikipedia.org/wiki/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
| [https://en.wikipedia.org/wiki/Inverter_(logic_gate) NOT] || ¬ / ′ || Ā || Output is the logical inverse of the input
|-
|-
| [[NAND gate|NAND]] || ↑ || ¬(A · B) || Complement of AND; universal gate
| [https://en.wikipedia.org/wiki/NAND_gate NAND] || ↑ || ¬(A · B) || Complement of AND; universal gate
|-
|-
| [[NOR gate|NOR]] || ↓ || ¬(A + B) || Complement of OR; universal gate
| [https://en.wikipedia.org/wiki/NOR_gate NOR] || ↓ || ¬(A + B) || Complement of OR; universal gate
|-
|-
| [[XOR gate|XOR]] || ⊕ || A ⊕ B || Output is 1 when inputs ''differ''
| [https://en.wikipedia.org/wiki/XOR_gate XOR] || ⊕ || A ⊕ B || Output is 1 when inputs ''differ''
|-
|-
| [[XNOR gate|XNOR]] || ⊙ || ¬(A ⊕ B) || Output is 1 when inputs are ''equal''
| [https://en.wikipedia.org/wiki/XNOR_gate XNOR] || ⊙ || ¬(A ⊕ B) || Output is 1 when inputs are ''equal''
|}
|}


=== Logic Algebra ===
=== Logic Algebra ===
 
The operation of [https://en.wiktionary.org/wiki/logic logic] circuits is governed by '''logic algebra''' ([https://en.wikipedia.org/wiki/Boolean_algebra Boolean algebra]), a formal [https://en.wiktionary.org/wiki/system system] in which [https://en.wiktionary.org/wiki/variable variables] take only the values 0 or 1, and [https://en.wiktionary.org/wiki/expression expressions] are evaluated using logical [https://en.wiktionary.org/wiki/operator operators]. Key identities include:
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:
* '''[https://en.wikipedia.org/wiki/Identity_element Identity laws]:''' A + 0 = A ;  A · 1 = A
 
* '''[https://en.wikipedia.org/wiki/Absorbing_element Null laws]:''' A + 1 = 1 ;  A · 0 = 0
* '''Identity laws:''' A + 0 = A ;  A · 1 = A
* '''[https://en.wikipedia.org/wiki/Idempotence Idempotent laws]:''' A + A = A ;  A · A = A
* '''Null laws:''' A + 1 = 1 ;  A · 0 = 0
* '''[https://en.wikipedia.org/wiki/Complement_(set_theory) Complement laws]:''' A + Ā = 1 ;  A · Ā = 0
* '''Idempotent laws:''' A + A = A ;  A · A = A
* '''[https://en.wikipedia.org/wiki/De_Morgan%27s_laws De Morgan's theorems]:''' ¬(A · B) = Ā + B̄ ;  ¬(A + B) = Ā · B̄
* '''Complement laws:''' A + Ā = 1 ;  A · Ā = 0
These identities allow engineers to simplify complex circuit [https://en.wiktionary.org/wiki/expression expressions], minimize [https://en.wiktionary.org/wiki/gate gate] count, and optimize [https://en.wiktionary.org/wiki/performance performance], a process formally known as [https://en.wikipedia.org/wiki/Logic_minimization logic minimization].
* '''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 ===
=== Types of Logic Circuits ===
 
Logic circuits are broadly classified into two [https://en.wiktionary.org/wiki/category categories]:
Logic circuits are broadly classified into two categories:
; [https://en.wikipedia.org/wiki/Combinational_logic Combinational Logic Circuits]
 
: The [https://en.wiktionary.org/wiki/output output] at any instant depends ''only'' on the current [https://en.wiktionary.org/wiki/combination combination] of [https://en.wiktionary.org/wiki/input inputs]. They contain no [https://en.wiktionary.org/wiki/memory memory] or [https://en.wiktionary.org/wiki/feedback feedback] elements. Examples include [https://en.wikipedia.org/wiki/Adder_(electronics) adders], [https://en.wikipedia.org/wiki/Multiplexer multiplexers], [https://en.wikipedia.org/wiki/Binary_decoder decoders], and [https://en.wikipedia.org/wiki/Comparator comparators].
; [[Combinational logic|Combinational Logic Circuits]]
; [https://en.wikipedia.org/wiki/Sequential_logic Sequential 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]].
: The output depends on both the current inputs ''and'' the history of past inputs, stored in internal [https://en.wikipedia.org/wiki/Flip-flop_(electronics) flip-flops] or [https://en.wikipedia.org/wiki/Latch_(electronics) latches]. Examples include [https://en.wikipedia.org/wiki/Counter_(digital) counters], [https://en.wikipedia.org/wiki/Shift_register shift registers], and [https://en.wikipedia.org/wiki/Finite-state_machine finite-state machines].
 
; [[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 ===
=== Implementation Technologies ===
 
Modern [https://en.wiktionary.org/wiki/logic logic] circuits are [https://en.wiktionary.org/wiki/implemented implemented] using a variety of [https://en.wiktionary.org/wiki/technology technologies]:
Modern logic circuits are implemented using a variety of technologies:
* '''[https://en.wikipedia.org/wiki/Transistor%E2%80%93transistor_logic Transistor-transistor logic] (TTL)''' — a legacy [https://en.wiktionary.org/wiki/bipolar bipolar] [https://en.wiktionary.org/wiki/transistor transistor] family widely used from the 1960s through the 1990s.
 
* '''[https://en.wikipedia.org/wiki/CMOS CMOS] (Complementary Metal-Oxide-Semiconductor)''' — the dominant [https://en.wiktionary.org/wiki/technology technology] in contemporary [https://en.wikipedia.org/wiki/Integrated_circuit integrated circuits], prized for low [https://en.wiktionary.org/wiki/power power] [https://en.wiktionary.org/wiki/consumption consumption].
* '''[[Transistor–transistor logic]] (TTL)''' — a legacy bipolar transistor family widely used from the 1960s through the 1990s.
* '''[https://en.wikipedia.org/wiki/Programmable_logic_device PLDs] and [https://en.wikipedia.org/wiki/Field-programmable_gate_array FPGAs]''' — [https://en.wiktionary.org/wiki/reconfigurable reconfigurable] [https://en.wiktionary.org/wiki/device devices] allowing logic circuits to be defined and modified in [https://en.wiktionary.org/wiki/software software].
* '''[[CMOS]] (Complementary Metal-Oxide-Semiconductor)''' — the dominant technology in contemporary integrated circuits, prized for low power consumption.
* '''[https://en.wikipedia.org/wiki/Application-specific_integrated_circuit ASICs]''' — custom-fabricated circuits [https://en.wiktionary.org/wiki/optimized optimized] for a specific [https://en.wiktionary.org/wiki/application application].
* '''[[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 ===
=== See Also ===
 
* [https://en.wikipedia.org/wiki/Boolean_algebra Boolean algebra]
* [[Boolean algebra]]
* [https://en.wikipedia.org/wiki/Digital_electronics Digital electronics]
* [[Digital electronics]]
* [https://en.wikipedia.org/wiki/Logic_gate Logic gate]
* [[Logic gate]]
* [https://en.wikipedia.org/wiki/Combinational_logic Combinational logic]
* [[Combinational logic]]
* [https://en.wikipedia.org/wiki/Sequential_logic Sequential logic]
* [[Sequential logic]]
* [https://en.wikipedia.org/wiki/Integrated_circuit Integrated circuit]
* [[Integrated circuit]]
* [https://en.wikipedia.org/wiki/Truth_table Truth table]
* [[Truth table]]
* [https://en.wikipedia.org/wiki/Karnaugh_map Karnaugh map]
* [[Karnaugh map]]
 
=== References ===
 
{{reflist}}


=== Further Reading ===
=== Further Reading ===
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