Logic Gates, Boolean Algebra and Karnaugh Maps

Challenge! By the end of todays session can you complete the following?

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

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

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

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

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

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

Define problems using Boolean logic Boolean algebra 1.Match the symbol to the operator. AND OR NOT XOR ∧ ¬ ∨ ⊻ ⊕

Define problems using Boolean logic Boolean algebra Use the correct symbols to define the following Boolean expressions: A ^ ¬ D V C V B BV CV B ¬ V ¬A D C B V ^ ^ ^B¬ B^ C V¬ D ¬ V V C VD V AC ^D ^ V A V ¬C ^ D ^ C B

Manipulate Boolean expressions, including the use of Karnaugh maps to simplify Boolean expressions Boolean algebra 1.What expression does this Karnaugh map illustrate? ABAB A 01 B

Manipulate Boolean expressions, including the use of Karnaugh maps to simplify Boolean expressions Boolean algebra 2. What expression does this Karnaugh map illustrate? ¬B ABAB A 01 B

Manipulate Boolean expressions, including the use of Karnaugh maps to simplify Boolean expressions Boolean algebra 3. What expression does this Karnaugh map illustrate? A¬^B ABAB A 01 B

Manipulate Boolean expressions, including the use of Karnaugh maps to simplify Boolean expressions Boolean algebra 4. What expression does this Karnaugh map illustrate? A^B ABAB A 01 B

Manipulate Boolean expressions, including the use of Karnaugh maps to simplify Boolean expressions Boolean algebra 5. What expression does this Karnaugh map illustrate?¬A^B ABAB A 01 B

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

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

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

Manipulate Boolean expressions, including the use of Karnaugh maps to simplify Boolean expressions Boolean algebra 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 AB C

Manipulate Boolean expressions, including the use of Karnaugh maps to simplify Boolean expressions Boolean algebra 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 AB C

Manipulate Boolean expressions, including the use of Karnaugh maps to simplify Boolean expressions Boolean algebra 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 AB C

Manipulate Boolean expressions, including the use of Karnaugh maps to simplify Boolean expressions Boolean algebra 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. 2.(A V B)^D CD AB

Manipulate Boolean expressions, including the use of Karnaugh maps to simplify Boolean expressions Boolean algebra 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 V ¬A ^ D CD AB

Manipulate Boolean expressions, including the use of Karnaugh maps to simplify Boolean expressions Boolean algebra 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. ¬C ^ ¬D V A CD AB

Manipulate Boolean expressions, including the use of Karnaugh maps to simplify Boolean expressions Boolean algebra 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

Manipulate Boolean expressions, including the use of Karnaugh maps to simplify Boolean expressions Boolean algebra 5. What is the expression shown in the Karnaugh map? ¬C V A^B CD AB

Manipulate Boolean expressions, including the use of Karnaugh maps to simplify Boolean expressions Boolean algebra 6. What is the expression shown in the Karnaugh map? ¬A ^ B ^ C ^ D v A ^ B ^ ¬ C ^ D CD AB

Challenge! Can you do it yet? AB C Simplify the following: (A ∧ B ∧ C) ∨( A ∧ ¬B ∧ C) ∨( A ∧ B ∧ ¬C) (A^B) V (A^C) A^(B V C)