Electronic – meant by taking dual of a boolean expression

boolean-algebradigital-logiclogic-gatessop

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?

Best Answer

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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