14:332:231 Lecture Notes - Lecture 3: Logic Gate, Summation, Logic Optimization
18 Jul 2018
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Use positive-logic convention, where 0 is low and 1 is high. We only need to include x in the expression. If the subexpression x*y + x*y" appears in an expression, we can then. Combining theorem (t10) replace it with just x. The y*z term is called the consensus of x*y and x"*z. If y*z is 1, then either x*y or x"*z must also be one. Therefore, term y*z is redundant and can be dropped. Most of these theorems can be proved using a two-step method called finite induction. First proving the theorem is true for n=2. Then proving the theorem is true for n=i and n=i+1 ( induction step ) Bubble pushing is the circuit demonstration of demorgan"s theorem. Push the bubbles from right to left, output to input. If there is a bubble in the output, it goes to both inputs. When a bubble is pushed, the gate is changed from or to and or and to or.
