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.

• 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.

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.