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Logic Gates, Boolean Algebra and Karnaugh Maps. Challenge! By the end of todays session can you complete the following?

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Presentation on theme: "Logic Gates, Boolean Algebra and Karnaugh Maps. Challenge! By the end of todays session can you complete the following?"— Presentation transcript:

1 Logic Gates, Boolean Algebra and Karnaugh Maps

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

3 Using logic gate diagrams and truth tables Boolean algebra 1.Complete the truth table for the following logic diagram: ABCD 0001 0101 1001 1110 A B C D

4 Using logic gate diagrams and truth tables Boolean algebra 2.Complete the truth table for the following logic diagram: ABCD 0011 0111 1000 1101 A B C D

5 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 00000 01011 10011 11011 00101 01111 10111 11111

6 Using logic gate diagrams and truth tables Boolean algebra 4.Complete the truth table for the following logic diagram: ABCDEF 000010 010111 100111 110111 001000 011100 101100 111100 A B C D E F

7 Using logic gate diagrams and truth tables Boolean algebra 5.Complete the truth table for the following logic diagram: ABCDEF 000101 001110 010110 011110 100000 101011 110011 111011 A B C D E F

8 Using logic gate diagrams and truth tables Boolean algebra 6.Complete the truth table for the following logic diagram: ABCDEF 000011 001001 010110 011101 100110 101101 110011 111001 A B C D E F

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

10 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

11 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 001 101

12 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 011 100

13 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 011 110

14 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 000 101

15 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 000 110

16 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 00011110 C 00010 11111

17 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 00011110 C 01111 10100

18 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 00011110 C 01000 11111

19 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 00011110 C 01100 11111

20 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 00011110 C 01111 11001

21 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 00011110 C 01000 11111

22 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 00011110 00 0111 1111 1011

23 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 00011110 000110 011111 110000 100000

24 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 00011110 001000 011000 111111 101111

25 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 00011110 001001 010000 110000 101001

26 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 00011110 0011 0111 111111 1011

27 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 00011110 00 011 111 10

28 Challenge! Can you do it yet? AB C 00011110 0 0010 1 0011 Simplify the following: (A ∧ B ∧ C) ∨( A ∧ ¬B ∧ C) ∨( A ∧ B ∧ ¬C) (A^B) V (A^C) A^(B V C)

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