Logic Circuit: Difference between revisions

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=== 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 ===

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 === 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]:''' &not;(A · B) = Ā + B̄ ;  &not;(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:''' &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 ===