DeMorgan's Theorem

Show in Gates 显示在盖茨

The most important logic theorem for digital electronics, this theorem says that any logical binary expression remains unchanged if we

1. Change all variables to their complements.
   将所有变量改为它们的补集
2. Change all AND operations to ORs.
   将所有 AND 运算改为 ORs。
3. Change all OR operations to ANDs.
   将所有OR操作转换为ANDs
4. Take the complement of the entire expression.
   对整个表达式取补集

A practical operational way to look at DeMorgan's Theorem is that the inversion bar of an expression may be broken at any point and the operation at that point replaced by its opposite (i.e., AND replaced by OR or vice versa).

DeMorgan's Theorem in Gates

Two forms of DeMorgan's Theorem implemented with basic gates.

DeMorgan Applications

DeMorgan's Theorem is useful in the implementation of the basic gate operations with alternative gates, particularly with NAND and NOR gates which are readily available in IC form.