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IMPLY gate

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Digital logic gate
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Input
A   B
Output
A → B
001
011
100
111

TheIMPLY gate is a digitallogic gate that implements alogical conditional.[1]

Symbols

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IMPLY can be denoted in algebraic expressions with thelogic symbol right-facing arrow (→). Logically, it is equivalent tomaterial implication, and the logical expression ¬A v B.

There are two symbols for IMPLY gates: the traditional symbol and theIEEE symbol. For more information seeLogic gate symbols.

Traditional IMPLY SymbolIEEE IMPLY Symbol

Functional completeness

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While the Implication gate is notfunctionally complete by itself, it is in conjunction with the constant 0 source. This can be shown via the following:

A0:=¬A(A0)B=¬(¬A)B=AB.{\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.

See also

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Wikimedia Commons has media related toIMPLY_gates.

References

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  1. ^"Implication Logic".Devices and Circuits for Stateful Logic and Memristive Sensing Applications. Retrieved3 November 2025.

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