Editing Propositional formula (section)

=== Engineering connectives ===
[[File:Propositional formula connectives 1.png|313px|thumb|right| Engineering symbols have varied over the years, but these are commonplace. Sometimes they appear simply as boxes with symbols in them. "a" and "b" are called "the inputs" and "c" is called "the output".]]

In general, the engineering connectives are just the same as the mathematics connectives excepting they tend to evaluate with "1" = "T" and "0" = "F". This is done for the purposes of analysis/minimization and synthesis of formulas by use of the notion of ''minterms'' and [[Karnaugh map]]s (see below). Engineers also use the words '''logical product''' from [[Boole]]'s notion (a*a = a) and '''logical sum''' from [[William Stanley Jevons|Jevons]]' notion (a+a = a).<ref>While the notion of logical product is not so peculiar (e.g. 0*0=0, 0*1=0, 1*0=0, 1*1=1), the notion of (1+1=1 ''is'' peculiar; in fact (a "+" b) = (a + (b - a*b)) where "+" is the "logical sum" but + and - are the true arithmetic counterparts. Occasionally all four notions do appear in a formula: A AND B = 1/2*( A plus B minus ( A XOR B ) ] (cf p. 146 in John Wakerly 1978, ''Error Detecting Codes, Self-Checking Circuits and Applications'', North-Holland, New York, {{isbn|0-444-00259-6}} pbk.)</ref>

{|class="wikitable" style="text-align:center"
|- style="font-size:9pt" 
|  Height="12" | 
|  | 
|  | 
|  | 
|  | 
! rowspan="2"  | logical product
! rowspan="2"  | logical sum
|  | 
|  | 
!  | half-adder<br/>(no carry)
|- style="font-size:9pt" 
| Height="12" | 
| 
| 
| 
| 
| 
| 
! exclusive OR
|- style="font-size:9pt" 
! Height="12" | row number
! colspan="2" | variables
|style="background-color:#EAF1DD" | NOT
|style="background-color:#EAF1DD" | NOT
|style="background-color:#DBE5F1" | AND
|style="background-color:#FDE9D9" | OR
| NAND
| NOR
| XOR
|-  
|style="font-size:9pt;white-space:nowrap;" Height="12" | b*2<sup>1</sup>+a*2<sup>0</sup>
|style="font-size:9pt;font-weight:bold" | b
|style="font-size:9pt;font-weight:bold" | a
|style="background-color:#EAF1DD;font-size:9pt;font-weight:bold;white-space:nowrap;" | ~(b)
|style="background-color:#EAF1DD;font-size:9pt;font-weight:bold;white-space:nowrap;" | ~(a)
|style="background-color:#DBE5F1;font-size:9pt;font-weight:bold;white-space:nowrap;" | (b & a)
|style="background-color:#FDE9D9;font-size:9pt;font-weight:bold;white-space:nowrap;" | (b &or; a)
|style="font-size:9pt;font-weight:bold;white-space:nowrap;" | ~(b & a)
|style="font-size:9pt;font-weight:bold;white-space:nowrap;" | ~(b &or; a)
|style="font-size:14pt" | ⊕
|-  
|style="font-size:9pt" Height="12" | 0
| 0
| 0
|style="background-color:#EAF1DD" | 1
|style="background-color:#EAF1DD" | 1
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|style="font-size:9pt" | 1
|style="font-size:9pt" | 0
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|style="font-size:9pt" | 1
|style="font-size:9pt" | 0
|style="font-size:9pt" | 1
|-  
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| 0
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|}