IMPLY gate

Input A B		Output A → B
0	0	1
0	1	1
1	0	0
1	1	1

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.


Traditional IMPLY Symbol		IEEE IMPLY Symbol

Functional completeness

While the Implication gate isn't functionally complete by itself, it is in conjunction with the constant 0 source. This can be shown via the following:

${\begin{aligned}A\rightarrow 0&:=\neg A\\(A\rightarrow 0)\rightarrow B&=\neg (\neg A)\lor B\\&=A\lor B.\end{aligned}}$

Thus as 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.

v t e Common logical connectives
Tautology/True $\top$
Alternative denial (NAND gate) $\uparrow$ Converse implication $\leftarrow$ Implication (IMPLY gate) $\rightarrow$ Disjunction (OR gate) $\lor$
Negation (NOT gate) $\neg$ Exclusive or (XOR gate) $\not \leftrightarrow$ Biconditional (XNOR gate) $\leftrightarrow$ Statement (Digital buffer)
Joint denial (NOR gate) $\downarrow$ Nonimplication (NIMPLY gate) $\nrightarrow$ Converse nonimplication $\nleftarrow$ Conjunction (AND gate) $\land$
Contradiction/False $\bot$
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Symbols

Functional completeness

See also