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

I explained De Morgan’s Law earlier. In this tutorial, I will solve some problems on this topic. There is another important technique, that should be addressed in this topic. This technique is known as the bubble-pushing technique.

Learning Objectives:

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

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

The bubble-pushing technique is related to De Morgan’s Theorem, which is directly applied to circuits containing NAND or NOR gates.

Bubble Pushing, Boolean Algebra for digital circuits
Example 1: Step by step guide: How to use bubble-pushing technique
Bubble Pushing, Boolean Algebra for digital circuits
Example 2: Step by step guide: How to use bubble-pushing technique

Solved Examples On Bubble-Pushing:

There are 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:

\(\overline{A+B}\)

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: \(\overline {A.B.C} \)

\(= \bar A + \bar B + \bar C \)
Bubble Pushing, Boolean Algebra for digital circuits

 

 

 

 

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

= A + (B + C)
 
= A + B . C
Bubble Pushing, Boolean Algebra for digital circuits

 

 

 

 

 

 

 

Example 6: AB + CD

[overline{AB}+overline{CD}]
 
[=bar A+bar B+ bar C + bar D]
 
Bubble Pushing, Boolean Algebra for digital circuits

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]
 
 
Bubble Pushing, Boolean Algebra for digital circuits

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

[=overline{AB} . overline{CD}]
[=(bar A + bar B).(bar C + bar D)]
 
Bubble Pushing, Boolean Algebra for digital circuits
 
 

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