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I read online that if we have a set of SOP terms giving a boolean expression, then the POS terms of the complement of the SOP terms will give the same expression. POS(f)=SOP(f').

This is called taking the dual of the expression. How does this work?

If I have: f = BD + AC + CE

Its complement: f' = (B' + D')(A' + C')(C' + E')

What is meant by taking the dual of f, and how do we get f in POS form?

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The dual of a boolean expression is an expression that is obtained following these steps:

  • replace any logical sum (OR) with a logical product (AND)
  • replace any logical product (AND) with a logical sum (OR)
  • replace any 0 constant with a 1 constant
  • replace any 1 constant with a 0 constant

The two basic logical operations AND and OR are called dual of each other, i.e. AND is the dual operation of OR and viceversa. Hence the dual transformation can be explained as:

Replace any operation with its dual and any constant with its complement (negation).

Note that negations must not be changed.

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  • \$\begingroup\$ Huh? This appears to contradict itself. "Replace .... any constant with its complement (negation)." but "Note that negations must not be changed." Can someone elaborate? \$\endgroup\$
    – nickalh
    Commented Mar 8, 2023 at 19:44
  • \$\begingroup\$ @nickalh Please, reread well. There's no contradiction: constants must be replaced with their negation, as explained above: 0 with 1 and 1 with 0, but negations (i.e. NOT operators) must not be touched. \$\endgroup\$ Commented Mar 10, 2023 at 10:24
  • \$\begingroup\$ still an example, probably 1 example with both literals and variables would clarify. \$\endgroup\$
    – nickalh
    Commented Mar 10, 2023 at 15:46

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