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Expert-verified Found in: Page 841 ### Discrete Mathematics and its Applications

Book edition 7th
Author(s) Kenneth H. Rosen
Pages 808 pages
ISBN 9780073383095 # $$a)$$ Draw a $$K{\bf{ - }}$$map for a function in two variables and put a $$1$$ in the cell representing $$\bar xy$$.$$b)$$ What are the minterms represented by cells adjacent to this cell$$?$$

$$(a)$$ The K-map for a function in two variables $$(b)$$The adjacent cells have minterms $$xy$$ and $$\bar x\bar y$$.

See the step by step solution

## Step 1:Definition

(a)

To reduce the number of terms in a Boolean expression representing a circuit, it is necessary to find terms to combine. There is a graphical method, called a Karnaugh map or K-map, for finding terms to combine for Boolean functions involving a relatively small number of variables. It will first illustrate how K-maps are used to simplify expansions of Boolean functions in two variables. It will continue by showing how K-maps can be used to minimize Boolean functions in three variables and then in four variables. Then it will describe the concepts that can be used to extend K-maps to minimize Boolean functions in more than four variables.

A $$K{\bf{ - }}$$map for a function in two variables is basically a table with two columns $$y$$ and $$\bar y$$ and two rows $$x$$ and $$\bar x$$.

(b)

Itplaces a $$1$$ in the cell corresponding to $$\bar xy$$ (which is the in the cell in the row $$\bar x$$ and in the column $$y$$). The minterms represented by the adjacent cells (to the cell with a $$1$$) are then the Boolean product of the row title and the column title of the cell.

It then notes that the adjacent cells have minterms $$xy$$ and $$\bar x\bar y$$.  ### Want to see more solutions like these? 