Lesson 0010: Continuation of Boolean Expression Notation

• NOR
• Is an operator that means not or.
• It is represented by the symbol of a not (~) in front of the OR-ed expression.
• Example: A NOR B is written .
• NAND
• Is an operator that means not and.
• It is represented by the symbol of a not (~) in front of the AND-ed expression.
• Example: A NAND B is written or .
• XOR
• Is an operator that stands for exclusive or.
• Is true when one or the other but NOT both inputs are true.
• It is represented by the symbol .
• EQUIV
• Is an operator that stands for equivalent.
• The output is true when the outputs are equivalent.
• It is represented by the symbol of a not (~) in front of the equation being XOR-ed.

The Rules

• NOR
• The output is true if both of the inputs are false.
• The output is false if either one of the inputs is true or if both of the inputs are true.
• NAND
• The output is true if both of the inputs are false or if either one of the inputs is false.
• The output is false if both of the inputs are true.
• XOR
• The output is true when the two inputs are not equivalent (one is false, one is true).
• The output is false when the two inputs are the same, either both are 0 or both are 1. (one or the other but NOT both)
• EQUIV
• The output is true when the two inputs are equivalent, or the same (both are true or both are false).
• The output is false when two inputs are not the same, one is false while one is true.

Check Up

What is the following operation the same as?

Well, there are two ways to go about this problem. We can look at it and simplify it using boolean algebra, or we can look at it from a logical perspective. Always look at it from a logical perspective before you begin using boolean algebra.

We can see here that we have a NOT operation on an A OR B. But then we see that NOT-ed again. If we think about it, if we do NOT(NOT A) then the answer is just A. So, NOT(NOT(A OR B)) just is A OR B.

1. What is the following expression equal to when A is true and B is false?

1
0

2. If A and B are both the same, the answer is true and if they are different, the answer is false, what is the boolean expression?
A NOR B
A NAND B
A EQUIV B
A XOR B

3. What operation is being used in the following equation?

A NOR B
A NAND B
A XOR B
none of the above

4. Give the result of the following expression if A is true, B is true,and C is false.

1
0

5. Which one of the following operations is an EQUIV operation?

none of the above

6. What two operators form the NOR operation?

XOR and NOT
OR and AND
OR and NOT
none of the above

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