# 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.

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

\(= \bar A + \bar B + \bar C \)#### 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)]