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Simplify of products, using the Karnaugh MAP below: the Boolean Bum AB ABC5 ABCD ABCD AB CE AB ABCD ABCD ABCD ABCD AB ABCD ABCD AB ABCO ABCO ABCD ABCD CD CD ABCD ABCD CD ABCD + Ā BCD t A B Ĉ D + Ā B

Simplify of products, using the Karnaugh MAP below: the Boolean Bum AB ABC5 ABCD ABCD AB CE AB ABCD ABCD ABCD ABCD AB ABCD ABCD AB ABCO ABCO ABCD ABCD CD CD ABCD ABCD CD ABCD + Ā BCD t A B Ĉ D + Ā B

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**Simplifying Boolean Expressions Using a Karnaugh Map** The task is to simplify the Boolean sum of products using the Karnaugh Map displayed. ### Karnaugh Map Layout: The Karnaugh map is organized as follows: - Columns represent values of variables AB, with possible states: - 00 - 01 - 11 - 10 - Rows represent values of variables CD, with possible states: - 00 - 01 - 11 - 10 The map contains the following marked cells representing the minterms of the equation: ``` | AB = 00 | AB = 01 | AB = 11 | AB = 10 | --------------------------------------------------------- CD = 00 | ~AB~CD | AB~CD | ABCD | ~ABCD | --------------------------------------------------------- CD = 01 | ~A~BCD | ABCD | ~ABCD | ABCD | --------------------------------------------------------- CD = 11 | ABCD | ABCD | ABCD | ABCD | --------------------------------------------------------- CD = 10 | ABCD | ABCD | ~ABCD | ~ABCD | ``` ### Boolean Expression: The expression to simplify is: ``` ABCD + ~ABCD + AB~CD + ~A~BCD + ~ABCD ``` This expression is derived from the cells that are marked or contain a “1” in the Karnaugh map, indicating that these conditions satisfy the desired output. **Explanation:** - Each cell in the Karnaugh map corresponds to a minterm. - By grouping adjacent cells containing ones, you can simplify the logic expression. - The goal is to cover all marked cells using the fewest number of groups, combining terms where possible to minimize the expression. **Result:** After simplification, the Boolean expression can be rewritten in a reduced form, which will consist of the most simplified combination of the original variables. This involves finding common terms and eliminating redundant information.
Transcribed Image Text:**Simplifying Boolean Expressions Using a Karnaugh Map** The task is to simplify the Boolean sum of products using the Karnaugh Map displayed. ### Karnaugh Map Layout: The Karnaugh map is organized as follows: - Columns represent values of variables AB, with possible states: - 00 - 01 - 11 - 10 - Rows represent values of variables CD, with possible states: - 00 - 01 - 11 - 10 The map contains the following marked cells representing the minterms of the equation: ``` | AB = 00 | AB = 01 | AB = 11 | AB = 10 | --------------------------------------------------------- CD = 00 | ~AB~CD | AB~CD | ABCD | ~ABCD | --------------------------------------------------------- CD = 01 | ~A~BCD | ABCD | ~ABCD | ABCD | --------------------------------------------------------- CD = 11 | ABCD | ABCD | ABCD | ABCD | --------------------------------------------------------- CD = 10 | ABCD | ABCD | ~ABCD | ~ABCD | ``` ### Boolean Expression: The expression to simplify is: ``` ABCD + ~ABCD + AB~CD + ~A~BCD + ~ABCD ``` This expression is derived from the cells that are marked or contain a “1” in the Karnaugh map, indicating that these conditions satisfy the desired output. **Explanation:** - Each cell in the Karnaugh map corresponds to a minterm. - By grouping adjacent cells containing ones, you can simplify the logic expression. - The goal is to cover all marked cells using the fewest number of groups, combining terms where possible to minimize the expression. **Result:** After simplification, the Boolean expression can be rewritten in a reduced form, which will consist of the most simplified combination of the original variables. This involves finding common terms and eliminating redundant information.
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