IMPLY gate
Digital logic gate
The IMPLY gate is a digital logic gate that implements a logical conditional.
Symbols
IMPLY can be denoted in algebraic expressions with the logic symbol right-facing arrow (→). Logically, it is equivalent to material implication, and the logical expression ¬A v B.
There are two symbols for IMPLY gates: the traditional symbol and the IEEE symbol. For more information see Logic gate symbols.
Functional completeness
While the Implication gate is not functionally complete by itself, it is in conjunction with the constant 0 source. This can be shown via the following:
A
→
0
:=
¬
A
(
A
→
0
)
→
B
=
¬
(
¬
A
)
∨
B
=
A
∨
B
.
{\displaystyle {\begin{aligned}A\rightarrow 0&:=\neg A\\(A\rightarrow 0)\rightarrow B&=\neg (\neg A)\lor B\\&=A\lor B.\end{aligned}}}
Thus, since the implication gate with the addition of the constant 0 source can create both the NOT gate and the OR gate, it can create the NOR gate, which is a universal gate.
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