Don't-care term

In digital logic, a don't-care term 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. 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.[1] 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 circuit results (minimization). Examples of don't-care terms are the binary values 1010 through 1111 (10 through 15 in decimal) for a function that takes a binary-coded decimal (BCD) value, because a BCD value never takes on such values (so called pseudo-tetrades); in the pictures, the circuit computing the lower left bar of a 7-segment display can be minimized to a b + a c by an appropriate choice of circuit outputs for dcba=1010...1111.

Don't⋅care terms chosen to get minimal circuit
ba
dc
00011110
00 1001
01 0001
11 0001
10 1001
Karnaugh map for lower left segment
ba
dc
00011110
00 1001
01 0001
11 xxxx
10 10xx
Digits in 7-segment display
ba
dc
00011110
00
01
11
10

Don't-care terms are important to consider in minimizing logic circuit design, using Karnaugh maps and the Quine–McCluskey algorithm. Don't care optimization can also be used in the development of highly size-optimized assembly or machine code taking advantage of side effects.

X value

"Don't care" may also refer to an unknown value in a multi-valued logic system, in which case it may also be called an X value. In the Verilog hardware description language such values are denoted by the letter "X". In the VHDL hardware description language such values are denoted (in the standard logic package) by the letter "X" (forced unknown) or the letter "W" (weak unknown).[2]

An X value does not exist in hardware. In simulation, an X value can result from two or more sources driving a signal simultaneously, or the stable output of a flip-flop not having been reached. In synthesized hardware, however, the actual value of such a signal will be either 0 or 1, but will not be determinable from the circuit's inputs.[2]

Power-up states

Further considerations are needed for logic circuits that involve some feedback. That is, those circuits that depend on the previous output(s) of the circuit as well as its current external inputs. Such circuits can be represented by a state machine. It is sometimes possible that some states that are nominally can't-happen conditions can accidentally be generated during power-up of the circuit or else by random interference. In some cases, there is no combination of inputs that can exit the state machine into a normal operational state. The machine remains stuck in the power-up state or can be moved only between other can't-happen states in a walled garden of states. Such states, while nominally can't-happen, are not don't-care, and designers take steps either to ensure that they are really made can't-happen, or else if they do happen, that they are transitory and lead to a normal operational state.[3]

See also

References

  1. J.A. Strong, Basic Digital Electronics, pp. 28-29, Springer, 2013 ISBN 940113118X.
  2. David Naylor and Simon Jones (1997). Vhdl: A Logic Synthesis Approach. Springer. pp. 14–15, 219, 221. ISBN 0-412-61650-5.
  3. Ramayya Kumar, Thomas Kropf (eds), Theorem Provers in Circuit Design, Vol 2, p. 136, Springer Science & Business Media, 1995 ISBN 3540590471.
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