What is the expression for the following kmap? Assume the ? values are don't care values but if circled, they are 1. So assume 1100 has 1 instead of ?. What is the expression? The image depicts a 4x4 Karnaugh map, a tool used in digital electronics to simplify Boolean algebra expressions.### Description:- The map is a grid with cell values corresponding to a combination of binary variables.- **Labels:** - Across the top, the columns are labeled based on binary values of variables \( YZ \): `00, 01, 11, 10`. - Down the side, the rows are labeled based on binary values of variables \( WX \): `00, 01, 11, 10`.### Cell Values:- **Row 00, Column 00:** 0- **Row 00, Column 01:** 0- **Row 00, Column 11:** 1- **Row 00, Column 10:** 1- **Row 01, Column 00:** 1- **Row 01, Column 01:** 0- **Row 01, Column 11:** 0- **Row 01, Column 10:** 0- **Row 11, Column 00:** ?- **Row 11, Column 01:** ?- **Row 11, Column 11:** ?- **Row 11, Column 10:** ?- **Row 10, Column 00:** 1- **Row 10, Column 01:** 0- **Row 10, Column 11:** ?- **Row 10, Column 10:** ?### Notes:- The unspecified values are marked as `?`, indicating they are "don't care" conditions that can be used flexibly in logical simplifications.- The highlighted cells indicate regions of interest, possibly for simplifying the logic expression by grouping ones or don't-cares.This layout is commonly used for visualizing and minimizing logical relationships in binary systems through visual grouping.

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Introductory Circuit Analysis (13th Edition)

13th Edition

ISBN:9780133923605

Author:Robert L. Boylestad

Publisher:Robert L. Boylestad

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What is the expression for the following kmap? Assume the ? values are don't care values but if circled, they are 1. So assume 1100 has 1 instead of ?. What is the expression?

The image depicts a 4x4 Karnaugh map, a tool used in digital electronics to simplify Boolean algebra expressions.

### Description:
- The map is a grid with cell values corresponding to a combination of binary variables.
- **Labels:**
- Across the top, the columns are labeled based on binary values of variables \( YZ \): `00, 01, 11, 10`.
- Down the side, the rows are labeled based on binary values of variables \( WX \): `00, 01, 11, 10`.

### Cell Values:

- **Row 00, Column 00:** 0
- **Row 00, Column 01:** 0
- **Row 00, Column 11:** 1
- **Row 00, Column 10:** 1

- **Row 01, Column 00:** 1
- **Row 01, Column 01:** 0
- **Row 01, Column 11:** 0
- **Row 01, Column 10:** 0

- **Row 11, Column 00:** ?
- **Row 11, Column 01:** ?
- **Row 11, Column 11:** ?
- **Row 11, Column 10:** ?

- **Row 10, Column 00:** 1
- **Row 10, Column 01:** 0
- **Row 10, Column 11:** ?
- **Row 10, Column 10:** ?

### Notes:
- The unspecified values are marked as `?`, indicating they are "don't care" conditions that can be used flexibly in logical simplifications.
- The highlighted cells indicate regions of interest, possibly for simplifying the logic expression by grouping ones or don't-cares.

This layout is commonly used for visualizing and minimizing logical relationships in binary systems through visual grouping.

Expert Solution

Step 1

Given data,

the given problem is K-map with the don't care condition.

K-map

Karnaugh map or K-map is a map of a function used in a technique used for minimization or simplification of a Boolean expression. It results in a smaller number of logic-gate and inputs being used during the fabrication.

In numerous digital circuits and other practical problems, finding expressions that have minimum variables becomes a prerequisite. In such cases, minimization of Boolean expressions is possible that have 3, or 4 variables. It can be done using the Karnaugh map without using any theorems of Boolean algebra.

The K-map can easily take two forms, namely, Sum of Product or SOP and Product of Sum or POS, according to need of the problem. K-map is a representation that is table-like, but it gives more data than the TRUTH TABLE. Fill a grid of K-map with 1s and 0s, then solve it by creating various groups.

Don't care condition

The "Don't care" condition enables the use of the blank cells of a K-map to make a group of the variables.

To make a group of cells, the "don't care" cells are used as either 0 or 1, and if required, they can ignore.

The "don't care" mainly uses to make a large group of cells.

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