Logic Gates, Boolean Algebra and Karnaugh Maps

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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