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.