LOGIC GATES, BOOLEAN ALGEBRA
AND KARNAUGH MAPS
Boolean algebra
Using logic gate diagrams and truth tables
1. Complete the truth table for the following logic diagram:
A
C
B
A
B
C
D
0
0
0
1
0
1
0
1
1
0
0
1
1
1
1
0
D
Boolean algebra
Using logic gate diagrams and truth tables
2. Complete the truth table for the following logic diagram:
A
C
A
B
C
D
0
0
1
1
0
1
1
1
1
0
0
0
1
1
0
1
D
B
Boolean algebra
Using logic gate diagrams and truth tables
3. Complete the truth table for the following logic diagram:
A
D
B
E
C
A
B
C
D
E
0
0
0
0
0
0
0
1
0
1
0
1
0
1
1
0
1
1
1
1
1
0
0
1
1
1
0
1
1
1
1
1
0
1
1
1
1
1
1
1
Boolean algebra
Using logic gate diagrams and truth tables
4. Complete the truth table for the following logic diagram:
A
B
D
A
B
C
D
E
F
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
1
1
0
1
1
1
0
0
1
0
0
1
1
1
1
0
1
1
0
0
1
1
0
1
1
1
1
1
1
1
0
0
F
E
C
Boolean algebra
Using logic gate diagrams and truth tables
5. Complete the truth table for the following logic diagram:
A
D
F
E
B
A
B
C
D
E
F
0
0
0
1
0
1
0
0
1
1
1
0
0
1
0
1
1
0
0
1
1
1
1
0
1
0
0
0
0
0
1
0
1
0
1
1
1
1
0
0
1
1
1
1
1
0
1
1
C
Boolean algebra
Using logic gate diagrams and truth tables
6. Complete the truth table for the following logic diagram:
A
B
A
B
C
D
E
F
0
0
0
0
1
1
0
0
1
0
0
1
0
1
0
1
1
0
0
1
1
1
0
1
1
0
0
1
1
0
1
0
1
1
0
1
1
1
0
0
1
1
1
1
1
0
0
1
D
E
C
F
Boolean algebra
Define problems using Boolean logic
1. Match the symbol to the operator.
AND
¬
∨
OR
NOT
∧
⊻
⊕
XOR
Boolean algebra
Use the correct symbols to define the following
Boolean expressions:
Define problems using Boolean logic
1
A
^
2
3
¬
D
V
C
V
B
4
5
V
B
C
6
V
B
¬
V
7
¬
A
D
C
B
V
^
^
8
9
^
B
¬
V
¬
B
^
C
^
D
V
10
11
C
V
D
V
12
A
^
B
^
A
C
^
V
¬
C
C
^
D
V
¬
D
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
A
B
0
1
0
0
1
1
0
1
B
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
A
B
0
1
0
1
1
1
0
0
B
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
A
B
0
1
0
1
1
1
1
0
B
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
A
B
0
1
0
0
0
1
0
1
B
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
A
B
0
1
0
0
0
1
1
0
B
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
AB
AB
C
00
01
11
10
0
0
0
1
0
1
1
1
1
1
C
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
AB
AB
C
00
01
11
10
0
1
1
1
1
1
0
1
0
0
C
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
AB
AB
C
00
01
11
10
0
1
0
0
0
1
1
1
1
1
C
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
AB
AB
C
00
01
11
10
0
1
1
0
0
1
1
1
1
1
C
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
AB
AB
C
00
01
11
10
0
1
1
1
1
1
1
0
0
1
C
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
AB
AB
C
00
01
11
10
0
1
0
0
0
1
1
1
1
1
C
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
CD
AB
00
01
11
10
00
0
0
0
0
01
0
1
1
0
11
0
1
1
0
10
0
1
1
0
AB
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
CD
AB
00
01
11
10
00
0
1
1
0
01
1
1
1
1
11
0
0
0
0
10
0
0
0
0
AB
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
CD
AB
00
01
11
10
00
1
0
0
0
01
1
0
0
0
11
1
1
1
1
10
1
1
1
1
AB
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
CD
AB
00
01
11
10
00
1
0
0
1
01
0
0
0
0
11
0
0
0
0
10
1
0
0
1
AB
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
CD
AB
00
01
00
1
1
01
1
1
11
1
1
10
1
1
11
10
1
1
AB
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
00
01
11
10
1
1
10
CHALLENGE!
Simplify the following:
A∧B∧C∨A∧¬B∧C∨A∧B∧¬C
AB
00
01
11
10
0
0
0
1
0
1
0
0
1
1
C