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Questions and Answers
What is the primary purpose of a Karnaugh map?
What is the primary purpose of a Karnaugh map?
- To simplify Boolean expressions to their simplest form (correct)
- To create a truth table for complex expressions
- To calculate the number of input variables needed
- To visualize the output states of a digital circuit
Which of the following statements about grouping in a Karnaugh map is incorrect?
Which of the following statements about grouping in a Karnaugh map is incorrect?
- Groups should be as large as possible without violating rules.
- Overlapping groups are allowed within the K-map.
- Only one cell can represent multiple values. (correct)
- Groups can include cells from opposite sides of the map.
When simplifying using a Karnaugh map, which group size is not permitted?
When simplifying using a Karnaugh map, which group size is not permitted?
- Five cells (correct)
- Six cells
- Three cells
- Four cells
Which of the following rules about grouping in a Karnaugh map is true?
Which of the following rules about grouping in a Karnaugh map is true?
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In which situation is it permitted to wrap around groups on a Karnaugh map?
In which situation is it permitted to wrap around groups on a Karnaugh map?
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Study Notes
Karnaugh Map (K-map)
- A Karnaugh Map (K-map) is a visual method for simplifying Boolean expressions, ensuring the simplest possible Sum of Products (SOP) or Product of Sums (POS) expression.
- K-maps are similar to Truth Tables, presenting inputs and outputs. However, instead of columns and rows, K-maps have an array of cells representing binary values of the inputs.
- Cells are strategically arranged to simplify expressions by grouping them.
- K-maps are used for simplifying Boolean expressions, especially for expressions with 2, 3, or 4 variables.
K-map Simplification Rules
- Only ones are considered: Cells with a value of 1 represent minterms in the Boolean expression.
- No diagonals: Groups cannot be formed diagonally.
- Powers of two: Groups must contain a number of cells equal to a power of two (1, 2, 4, 8, etc.).
- Maximum group size: Groups should be as large as possible to simplify the expression.
- Every one included: All ones in the K-map must be included in at least one group.
- Overlapping allowed: Groups can overlap.
- Wrap around allowed: Groups can wrap around the edges of the K-map.
- Minimal groups: Aim for the smallest number of groups possible.
Looping and Variables
- Quads: A group of 4 cells represents a quad. After looping a quad, the resulting term will only include variables that remain constant across all squares in the quad.
Solving Examples
- Example 1: K-map with simplified expression.
- Example 2: K-map with simplified expression.
- Example 3: K-map with simplified expression.
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