๐ Bubble Pushing and Matching
We want to make logic gates more understandable to us by
- Shifting NOT gates away from outputs,
- Eliminating NOT gates that face each other from OUTPUT of one to the INPUT of another.
We will end up with an input-priority, simplified logic circuit
๐งช Shift NOT Gates away from Output
We can do this through shifting the negation from the output to the inputs, while also switching to the other fundamental logic gate (AND, OR)
This is the De Morganโs Law
| Original Expression | Transformed Expression |
|---|---|
| $\overline{A \cdot B}$ | $\overline{A} + \overline{B}$ |
| $\overline{A + B}$ | $\overline{A} \cdot \overline{B}$ |
We want to remove the negations on all the logic gates:
- Because negations from outputs can always pass backwards to their inputs, while it cannot always pass forwards to another input
- We will start from the ending logic gate and do negation flipping all the way until we reach the starting logic gates
Name Drop
This is also known as Bubble Pushing
Name Drop
This is also known as Bubble Pushing
๐ซง Eliminate NOT gates Facing Each Other
Sometimes negations at an output of a gate flows to the negation of the input of another
As negation works in a system of only 2 states, applying negations in pairs will result in no net change
Optimisation We can eliminate both the negations at the output of one and at where it flows into the input of another to reduce the number of unnecessary gates
๐ก
Name Drop
This is also known as Bubble Matching
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