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Cononical Forms of Boolean Expressions

Cononical Forms of Boolean Expressions. The Sum-of-products (SOP) Expressions. When two or more product terms (Boolean Multiplication) are summed by Boolean addition. For Example. AB + AD’ A + A’B’C + A’B’

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Cononical Forms of Boolean Expressions

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  1. Cononical Forms of Boolean Expressions

  2. The Sum-of-products (SOP) Expressions • When two or more product terms (Boolean Multiplication) are summed by Boolean addition. • For Example. • AB + AD’ • A + A’B’C + A’B’ Each SOP expression can be implemented by simply ORing the outputs of two or more AND gates. SOP expressions can be implemented by AND-OR realization. We can also implement SOP expressions with the help of NAND-NAND realization.

  3. The Sum-of-products (SOP) Expressions A AB B B BCD Y C D A AC C Y=AB + BCD + AC

  4. Same Example With NAND-NAND realization A (AB)’ B B (BCD)’ C Y D A (AC)’ C Y=((AB)’.(BCD)’.(AC)’)’   AB+BCD+AC (AB)’’+(BCD)’’+(AC)’’

  5. The Product-of-sums (POS) expressions • When two or more sum terms are multiplied by Boolean multiplication. • For Example. • (A+B) .(A+C’) • (A+B).(B+C+D’).(A’+C) Each POS expressions can be implemented by simply ANDing the outputs of two or more OR gates. POS expression can be implemented by OR-AND realization. POS expression can also be implemented with the help of NOR-NOR realization.

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