Introductory Circuit Analysis (13th Edition)
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Author: Robert L. Boylestad
Publisher: PEARSON
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Using Boolean Algebra laws, rules, and theorems, simplify the expressions below. Please use a whiteboard!
![The expression in the image is a Boolean algebra expression shown below:
\[\overline{A}BCD + BD + A\overline{B}D + \overline{B}D\]
### Explanation:
The expression features multiple terms that are combined using the OR (+) operation. Each term consists of variables that can either be in their normal form (e.g., \(A, B, C, D\)) or in their complemented form (e.g., \(\overline{A}, \overline{B}\)).
- **\(\overline{A}BCD\):** This term contains the complemented variable \(\overline{A}\) along with \(B, C, D\).
- **\(BD\):** This term includes variables \(B\) and \(D\).
- **\(A\overline{B}D\):** This term includes \(A, D\) and the complemented variable \(\overline{B}\).
- **\(\overline{B}D\):** This term consists of the complemented variable \(\overline{B}\) and \(D\).
This kind of expression is often used in digital logic design, circuit simplification, and can be minimized using Boolean algebra rules or Karnaugh maps.](https://content.bartleby.com/qna-images/question/7acc2a83-cedf-45e6-b77a-a907c03259d0/0e89f465-6397-4154-a4e7-86478d82dbe2/zkyasc8_processed.png)
Transcribed Image Text:The expression in the image is a Boolean algebra expression shown below:
\[\overline{A}BCD + BD + A\overline{B}D + \overline{B}D\]
### Explanation:
The expression features multiple terms that are combined using the OR (+) operation. Each term consists of variables that can either be in their normal form (e.g., \(A, B, C, D\)) or in their complemented form (e.g., \(\overline{A}, \overline{B}\)).
- **\(\overline{A}BCD\):** This term contains the complemented variable \(\overline{A}\) along with \(B, C, D\).
- **\(BD\):** This term includes variables \(B\) and \(D\).
- **\(A\overline{B}D\):** This term includes \(A, D\) and the complemented variable \(\overline{B}\).
- **\(\overline{B}D\):** This term consists of the complemented variable \(\overline{B}\) and \(D\).
This kind of expression is often used in digital logic design, circuit simplification, and can be minimized using Boolean algebra rules or Karnaugh maps.
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