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{{ba title|incompletely specified function}}
 
{{ba title|incompletely specified function}}
An '''Incompletely specified function''' is a [[Boolean function]] that only define output values for a subset of its inputs - i.e. a Boolean function whos output is a [[don't care]] for at least one of its input combinations. Incompletely specified functions often make no guarantees as to the unspecified output whatsoever.
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An '''Incompletely specified function''' is a [[Boolean function]] that only define output values for a subset of its inputs. For outputs that are not specified, the inputs are treated as [[don't care]] values. Incompletely specified functions often make no guarantees as to the unspecified output whatsoever.
  
 
==Overview==
 
==Overview==
{| class="wikitable" style="float: right; width: 140px; text-align: center;"
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In many situations when working with [[combinational circuit]]s, some combinations of inputs cannot occur or [[can't happen|should not occur]] under normal working conditions. For those combinations the output can be disregarded allowing for possibly further [[logic minimization]].
! A !! B !! C !! <math>f</math>
 
|-
 
| 0 || 0 || 0 || 1
 
|-
 
| 0 || 0 || 1 || {{X}}
 
|-
 
| 0 || 1 || 0 || {{X}}
 
|-
 
| 0 || 1 || 1 || 1
 
|-
 
| 1 || 0 || 0 || 1
 
|-
 
| 1 || 0 || 1 || 0
 
|-
 
| 1 || 1 || 0 || 0
 
|-
 
| 1 || 1 || 1 || {{X}}
 
|}
 
In many situations when working with [[combinational circuit]]s, some combinations of inputs [[can't happen|should not occur]] under normal working conditions. For circuits with such combinations, those combinations can be treated as either 0 or 1 depending on whichever yields a more [[logic minimization|simplified]] Boolean expression.
 
 
 
Boolean functions with don't care output terms are represented with a <math>d</math>. For example consider the following function.
 
::<math>f(A,B,C) = \sum m(0,3,4)+d(1,2,7)</math>
 
Which can be represented with the following [[truth table]] and [[K-map]].
 
 
 
::[[File:kmap unspecified func example.svg|200px]]
 
 
 
Note that depending on the final design of the circuit, the output for <math>f(0,0,1)</math> for example may be either 0 or 1.
 
 
 
== K-map ==
 
[[File:kmap (don't care example).svg|right|200px]]
 
{{main|karnaugh_map#Don't cares}}
 
Karnaugh maps are especially suitable for [[logic minimization|minimizing]] logic circuts with [[don't care]] outputs because they directly translate to don't care cells on a k-map. If grouping don't care cells results in larger groups, then more variables may be eliminated resulting in smaller Boolean expressions.
 
{{clear}}
 
 
 
== Properties ==
 
{{empty section}}
 

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