Editing Logic Circuit

== Logic Circuit ==

# A '''logic circuit''' is the primary control [https://en.wiktionary.org/wiki/information information] processor in [https://en.wiktionary.org/wiki/digital digital] equipment. It is composed of interconnected [https://en.wiktionary.org/wiki/electronic electronic] [https://en.wiktionary.org/wiki/gate gate]s whose collective operation is described by [https://en.wiktionary.org/wiki/equation equation]s drawn from a specialized branch of [https://en.wiktionary.org/wiki/mathematics mathematics] known as [https://en.wiktionary.org/wiki/Boolean_algebra Boolean algebra] (also called ''[https://en.wiktionary.org/wiki/logic logic] algebra'' or ''[https://en.wiktionary.org/wiki/switching 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 [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.

=== 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:
{| class="wikitable"
|-
! Gate !! Symbol !! Boolean Expression !! Description
|-
| [https://en.wikipedia.org/wiki/AND_gate AND] || · || A · B || Output is 1 only when ''all'' inputs are 1
|-
| [https://en.wikipedia.org/wiki/OR_gate OR] || + || A + B || Output is 1 when ''at least one'' input is 1
|-
| [https://en.wikipedia.org/wiki/Inverter_(logic_gate) NOT] || ¬ / ′ || Ā || Output is the logical inverse of the input
|-
| [https://en.wikipedia.org/wiki/NAND_gate NAND] || ↑ || &not;(A · B) || Complement of AND; universal gate
|-
| [https://en.wikipedia.org/wiki/NOR_gate NOR] || ↓ || &not;(A + B) || Complement of OR; universal gate
|-
| [https://en.wikipedia.org/wiki/XOR_gate XOR] || ⊕ || A ⊕ B || Output is 1 when inputs ''differ''
|-
| [https://en.wikipedia.org/wiki/XNOR_gate XNOR] || ⊙ || &not;(A ⊕ B) || Output is 1 when inputs are ''equal''
|}

=== 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:
* '''[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
* '''[https://en.wikipedia.org/wiki/Idempotence Idempotent laws]:''' A + A = A ;  A · A = A
* '''[https://en.wikipedia.org/wiki/Complement_(set_theory) Complement laws]:''' A + Ā = 1 ;  A · Ā = 0
* '''[https://en.wikipedia.org/wiki/De_Morgan%27s_laws De Morgan's theorems]:''' &not;(A · B) = Ā + B̄ ;  &not;(A + B) = Ā · B̄
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].

=== Types of Logic Circuits ===
Logic circuits are broadly classified into two [https://en.wiktionary.org/wiki/category 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].
; [https://en.wikipedia.org/wiki/Sequential_logic Sequential Logic Circuits]
: 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].

=== 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]:
* '''[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].
* '''[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].
* '''[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].

=== See Also ===
* [https://en.wikipedia.org/wiki/Boolean_algebra Boolean algebra]
* [https://en.wikipedia.org/wiki/Digital_electronics Digital electronics]
* [https://en.wikipedia.org/wiki/Logic_gate Logic gate]
* [https://en.wikipedia.org/wiki/Combinational_logic Combinational logic]
* [https://en.wikipedia.org/wiki/Sequential_logic Sequential logic]
* [https://en.wikipedia.org/wiki/Integrated_circuit Integrated circuit]
* [https://en.wikipedia.org/wiki/Truth_table Truth table]
* [https://en.wikipedia.org/wiki/Karnaugh_map Karnaugh map]

=== 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]]