Practical Electronics/Logic/Boolean Identities Summary
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Practical Electronics
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Logic
DeMorgan's Law
Name
Statement
Associative Law
A
⋅
B
⋅
C
=
(
A
⋅
B
)
⋅
C
=
A
⋅
(
B
⋅
C
)
{\displaystyle A\cdot B\cdot C=\left(A\cdot B\right)\cdot C=A\cdot \left(B\cdot C\right)}
Distributive Law
A
⋅
(
B
+
C
)
=
(
A
⋅
B
)
+
(
A
⋅
C
)
{\displaystyle A\cdot \left(B+C\right)=\left(A\cdot B\right)+\left(A\cdot C\right)}
Commutative Laws
A
⋅
B
=
B
⋅
A
{\displaystyle A\cdot B=B\cdot A}
A
+
B
=
B
+
A
{\displaystyle A+B=B+A\,}
A
⊕
B
=
B
⊕
A
{\displaystyle A\oplus B=B\oplus A}
DeMorgan's Law (1)
A
+
B
¯
=
A
¯
⋅
B
¯
{\displaystyle {\overline {A+B}}={\overline {A}}\cdot {\overline {B}}}
DeMorgan's Law (2)
A
⋅
B
¯
=
A
¯
+
B
¯
{\displaystyle {\overline {A\cdot B}}={\overline {A}}+{\overline {B}}}
