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Boolean Logic
Boolean Operators (T/F)x y x AND y
F F F
F T F
T F F
T T T
x y x OR y
F F F
F T T
T F T
T T T
x NOT x
F T
T F
Boolean Operators (1/0)x y x AND y
0 0 0
0 1 0
1 0 0
1 1 1
x y x OR y
0 0 0
0 1 1
1 0 1
1 1 1
x NOT x
0 1
1 0
More Boolean Operators (1/0)x y x NAND y
0 0 1
0 1 1
1 0 1
1 1 0
x y x NOR y
0 0 1
0 1 0
1 0 0
1 1 0
x y x XOR y
0 0 0
0 1 1
1 0 1
1 1 0
NAND = NOT(x AND y)NOR = NOT(x OR y)XOR = EXCLUSIVE OR
Boolean Expressions Follows a logical order of operations
1. NOT operators
2. Parentheses
3. AND
4. OR
Examples:x OR y AND z
x OR (y AND z) Do it this way just in case
Truth Tables Write out table of all
possible combinations of truth values
Evaluate the boolean expression for all combinations
Examplex OR y AND z
x y z x OR (y AND z)
F F F F
F F T F
F T F F
F T T T
T F F T
T F T T
T T F T
T T T T
Example What is the truth table for: NOT x OR y?
x y NOT x OR y
F F
F T
T F
T T
Another Example What is the truth table for: x AND NOT y?
x y x AND NOT y
F F
F T
T F
T T
Your Turn What is the truth table for the Boolean
expression: x OR NOT y OR z?
Your Turn What is the truth table for the Boolean
expression: x NAND y OR NOT z
Your turn What is the truth table for the Boolean
expression: a AND (b XOR c)
Partner Practice
1. Write a Boolean expression with no more than 3 variables (you can have multiple Boolean operators)
2. Swap boards with somebody else in the room
3. Write the truth table for the expression
Problem Scenarios
1. You will be given a scenario
2. Identify the input variables
3. Write the Boolean expression
4. Construct the truth table
Scenario #1 Either the sun is shining or rain is falling
1. Identify the input variables
2. Write the Boolean expression
3. Construct the truth table
Scenario #2 Maria won’t go to school if it is cold and
raining or she has not done her homework.
1. Identify the input variables
2. Write the Boolean expression
3. Construct the truth table
Scenario #3 Your car has 4 wheel drive, which turns on
when the temperature is freezing or when you hit the manual override, but you cannot turn on the override when you are going over 60 mph.
1. Identify the input variables
2. Write the Boolean expression
3. Construct the truth table
Scenario #4 You are ordering dinner, and your options
are a burger, fries, and vegetables. You cannot get a burger and a side of fries together. The healthy option of steamed vegetables is allowed with your burger.
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