De Morgan's Law and Bubble Pushing Solved Problems Step By Step

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Bubble Pushing| Bubble Logic |De Morgan's Law:

I have explained De Morgan's Law earlier. I'm this tutorial I am going to solve some problems on this topic. There is another important technique, which should be addressed in this topic. And this technique is known as bubble pushing technique. 

Learning Objectives:

• Learn more about bubble pushing technique with the help of solved examples

I will show step by step procedure for bubble logic or bubble pushing. There is a detailed explanation for two examples while rest are solved directly. With the the help of detailed explanation you will be able to evaluate directly as well.

Bubble pushing technique is related to De Morgan's Theorem, which is directly applied to circuits containing NAND or NOR gates.

Solved Examples:

Some useful tips to follow while solving these problems.

• Break the longest bar first
• Don't break the two bars at the same time
• After the bar breaks, change the operator ("+" to "." and "." to "+") underneath the bar. 

Example 1: \[\bar A + \bar B\]

\[\overline{A+B}\]

Example 2: \[\overline{\bar A. \bar B}\]

\[=\overline{\bar A}+ \bar B\]

\[=A+\bar B \text{ Rule 9}\]

 

Example 3: \[\overline{A+B+C}\]

\[=\bar A . \bar B. \bar C\]

Example 4: \[\overline{A.B.C}\]

\[=bar  A + \bar B + \bar C\]

Example 5: \[\overline{(B+C)A}\]

= A + (B + C)

= A + B . C

Example 6: AB + CD

\[\overline{AB}+\overline{CD}\]

\[=\bar A+\bar B+ \bar C + \bar D\]

Example 7: 

\[=\overline{(A+\bar B)(\bar C+D)}\]

\[=\overline{(A+\bar B)}.\overline{(\bar C+D)}\]

\[=\bar A. \overline{\bar B} + \overline{\bar C}.D\]

\[=\bar A.B + C.\bar D\]

Example 8:\[\overline{A.B+C.D}\]

\[=\overline{AB} . \overline{CD}\]

\[=(\bar A + \bar B).(\bar C + \bar D)\]