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๐Ÿ” Bubble Pushing and Matching

๐Ÿ” 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


๐Ÿงช 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 Morganโ€™s Law

Original ExpressionTransformed 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

๐Ÿซง 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

๐Ÿ’ก
Name Drop This is also known as Bubble Matching
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