6.1 DIGITAL BUILDING BLOCKS 277TABLE 6.1.2Logic Symbols and Truth Tables
The last two entries in Table 6.1.3 are known asDeMorgan’s theorems, whose importance
stems from the fact that they offer a general technique for complementing Boolean expressions.
They show that any logic function can be implemented using only OR and NOT gates, or using
only AND and NOT gates. There exists adualitybetween AND and OR operations; any function
can be realized by just one of the two basic operations, plus the complement operation. This gives
rise to two families of logic functions:sum of products(SOP) andproduct of sums(POS). Any
logic expression can be reduced to either one of these.