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Logic Gates, Boolean Algebra and Karnaugh Maps

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Presentation on theme: "Logic Gates, Boolean Algebra and Karnaugh Maps"— Presentation transcript:

1 Logic Gates, Boolean Algebra and Karnaugh Maps

2 Boolean algebra A B C D 1 Using logic gate diagrams and truth tables
Complete the truth table for the following logic diagram: A B C D 1 A C D B

3 Boolean algebra A B C D 1 Using logic gate diagrams and truth tables
Complete the truth table for the following logic diagram: A B C D 1 C A D B

4 Boolean algebra A B C D E 1 Using logic gate diagrams and truth tables
Complete the truth table for the following logic diagram: A B C D E 1 A D B E C

5 Boolean algebra A B C D E F 1
Using logic gate diagrams and truth tables Complete the truth table for the following logic diagram: A B C D E F 1 A B D F E C

6 Boolean algebra A B C D E F 1
Using logic gate diagrams and truth tables Complete the truth table for the following logic diagram: A B C D E F 1 A D F E B C

7 Boolean algebra A B C D E F 1
Using logic gate diagrams and truth tables Complete the truth table for the following logic diagram: A B C D E F 1 A B D F E C

8 ¬ ⊻ NOT AND ⊕ OR XOR ∨ ∧ Boolean algebra
Define problems using Boolean logic Match the symbol to the operator. ⊻ NOT AND ⊕ OR XOR ∨ ∧

9 Use the correct symbols to define the following Boolean expressions:
Boolean algebra Use the correct symbols to define the following Boolean expressions: Define problems using Boolean logic 1 A  ^ 2   D  V  C 3 B 4   V   C 5  ¬ 6 7  D 8 9 B  ^  10 C V  D   A 11 12  B

10 Boolean algebra Manipulate Boolean expressions, including the use of Karnaugh maps to simplify Boolean expressions 1. What expression does this Karnaugh map illustrate? > A A B 1

11 Boolean algebra Manipulate Boolean expressions, including the use of Karnaugh maps to simplify Boolean expressions 2. What expression does this Karnaugh map illustrate? > NOT B A B 1

12 Boolean algebra Manipulate Boolean expressions, including the use of Karnaugh maps to simplify Boolean expressions 3. What expression does this Karnaugh map illustrate? > NOT A OR NOT B A B 1

13 Boolean algebra Manipulate Boolean expressions, including the use of Karnaugh maps to simplify Boolean expressions 4. What expression does this Karnaugh map illustrate? > A AND B A B 1

14 Boolean algebra Manipulate Boolean expressions, including the use of Karnaugh maps to simplify Boolean expressions 5. What expression does this Karnaugh map illustrate? > NOT A AND B A B 1

15 Boolean algebra Manipulate Boolean expressions, including the use of Karnaugh maps to simplify Boolean expressions 1. Write the expression: A ∧ B ∨ C into the Karnaugh map, and draw rectangles/squares around the groups. AB C 00 01 11 10 1

16 Boolean algebra Manipulate Boolean expressions, including the use of Karnaugh maps to simplify Boolean expressions 2. Write the expression: ¬A ∧ B ∨ ¬C into the Karnaugh map, and draw rectangles/squares around the groups. AB C 00 01 11 10 1

17 Boolean algebra Manipulate Boolean expressions, including the use of Karnaugh maps to simplify Boolean expressions 3. Write the expression: ¬A ∧ ¬B ∨ C into the Karnaugh map, and draw rectangles/squares around the groups. AB C 00 01 11 10 1

18 Boolean algebra Manipulate Boolean expressions, including the use of Karnaugh maps to simplify Boolean expressions 4. Write the expression: ¬A ∧ ¬B ∨ ¬A ∧ B ∨ C into the Karnaugh map, and draw rectangles/squares around the groups. What is the simplified version of this expression? AB C 00 01 11 10 1

19 Boolean algebra Manipulate Boolean expressions, including the use of Karnaugh maps to simplify Boolean expressions 5. Write the expression: A ∧ ¬B ∨ ¬A ∧ ¬B ∨ ¬C into the Karnaugh map, and draw rectangles/squares around the groups. What is the simplified version of this expression? AB C 00 01 11 10 1

20 Boolean algebra Manipulate Boolean expressions, including the use of Karnaugh maps to simplify Boolean expressions 6. Write the expression: A ∧ B ∧ C ∨ ¬A ∧ ¬B ∨ C into the Karnaugh map, and draw rectangles/squares around the groups. What is the simplified version of this expression? AB C 00 01 11 10 1

21 Boolean algebra Manipulate Boolean expressions, including the use of Karnaugh maps to simplify Boolean expressions 1. Write the expression: A ∧ D ∨ B ∧ D ∨ A ∧ ¬B ∧ C ∧ D into the Karnaugh map, and draw rectangles/squares around the groups and show the simplified expression. > A ∧ D ∨ B ∧ D CD AB 00 01 11 10 1

22 Boolean algebra Manipulate Boolean expressions, including the use of Karnaugh maps to simplify Boolean expressions 2. Write the expression: ¬A ∧ B ∨ ¬A ∧ ¬B ∧ D ∨ ¬A ∧ D into the Karnaugh map, and draw rectangles/squares around the groups and show the simplified expression. > ¬A ∧ B ∨ ¬A ∧ D CD AB 00 01 11 10 1

23 Boolean algebra Manipulate Boolean expressions, including the use of Karnaugh maps to simplify Boolean expressions 3. Write the expression: A ∧ ¬B ∨ ¬C ∧ ¬D ∨ A ∧ B into the Karnaugh map, and draw rectangles/squares around the groups and show the simplified expression. > :A ∨ ¬C ∧ ¬D CD AB 00 01 11 10 1

24 Boolean algebra Manipulate Boolean expressions, including the use of Karnaugh maps to simplify Boolean expressions 4. Write the expression: ¬B ∧ ¬D ∨ A ∧ ¬B ∧ C ∧ ¬D into the Karnaugh map, and draw rectangles/squares around the groups and show the simplified expression. > ¬B ∧ ¬D CD AB 00 01 11 10 1

25 Boolean algebra Manipulate Boolean expressions, including the use of Karnaugh maps to simplify Boolean expressions 5. What is the expression shown in the Karnaugh map? > A ∧ B ∨ ¬C CD AB 00 01 11 10 1

26 Boolean algebra Manipulate Boolean expressions, including the use of Karnaugh maps to simplify Boolean expressions 6. What is the expression shown in the Karnaugh map? > ¬A ∧ B ∧ C ∧ D ∨ A ∧ B ∧ ¬C ∧ D CD AB 00 01 11 10 1

27 Challenge! Simplify the following: A∧B∧C∨A∧¬B∧C∨A∧B∧¬C AB C 00 01 11
10 1

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