Don't-care term

Not to be confused with Three-state logic.

In digital logic, a don't-care term[1][2] (abbreviated DC, historically also known as redundancies,[2] irrelevancies,[2] optional entries,[3][4] invalid combinations,[5][4][6] vacuous combinations,[7][4] forbidden combinations,[8][2] unused states or logical remainders[9]) for a function is an input-sequence (a series of bits) for which the function output does not matter. An input that is known never to occur is a can't-happen term.[10][11][12][13] Both these types of conditions are treated the same way in logic design and may be referred to collectively as don't-care conditions for brevity.[14] The designer of a logic circuit to implement the function need not care about such inputs, but can choose the circuit's output arbitrarily, usually such that the simplest, smallest, fastest or cheapest circuit results (minimization) or the power-consumption is minimized.[15][16]

Don't-care terms are important to consider in minimizing logic circuit design, including graphical methods like Karnaugh–Veitch maps and algebraic methods such as the Quine–McCluskey algorithm. In 1958, Seymour Ginsburg proved that minimization of states of a finite-state machine with don't-care conditions does not necessarily yield a minimization of logic elements. Direct minimization of logic elements in such circuits was computationally impractical (for large systems) with the computing power available to Ginsburg in 1958.[17]

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  2. ^ a b c d Cite error: The named reference Phister_1958 was invoked but never defined (see the help page).
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