A combinational ternary logic gate that is important as a building block in the synthesis of ternary logic circuits (see multivalued logic). An S-gate may have any number of inputs {a_i} and one output {s}, all of which can take values represented by elements of the set {0,1,2}. The function of the S-gate is given by

The reason for the name S-gate is because the French for threshold is seuil. The S-gate should not be confused with the ternary selector gate (T-gate). More complicated versions of the S-gate have been defined in various ways. See also threshold element.