4.2.1 : Not

Now that we've defined what a boolean statement is, let's start to do work with them. The NOT operator switches the value of the boolean statement. The boolean statement, "Carrots are healthy" evaluates to true. When we add a NOT operator, it becomes "Carrots are not healthy" which is a false statement. Now how do we represent this information? There are many ways to represent boolean algebra expressions. There's an algebraic notation which is a symbol used for expressions. Below is also the representation of an in/out circuit symbol. The table is a truth table. Truth tables are used to show every outcome of true and false statements and their operators. Since NOT only takes one input, there's only 2 posssible outcomes. We start with 0 as our first input then move onto 1. If we remember, 0 and 1 are the binary values for 0 and 1. Here, it's much harder to see, but as we move onto larger truth tables, we'll get move of an understanding on how they work.

Notation: ¬x , x'

x	¬x
0	1
1	0

{ "width":312, "height":108, "showToolbox":false, "devices":[ {"type":"DC","id":"dev0","x":52,"y":36,"label":"DC"}, {"type":"NOT","id":"dev1","x":164,"y":60,"label":"NOT"}, {"type":"LED","id":"dev2","x":220,"y":60,"label":"LED"}, {"type":"LED","id":"dev3","x":220,"y":12,"label":"LED"}, {"type":"Toggle","id":"dev4","x":108,"y":36,"label":"X"} ], "connectors":[ {"from":"dev1.in0","to":"dev4.out0"}, {"from":"dev2.in0","to":"dev1.out0"}, {"from":"dev3.in0","to":"dev4.out0"}, {"from":"dev4.in0","to":"dev0.out0"} ] }

NOT is the operator for negation. Like in basic algebra, we know the negative sign is for negation. So if we apply a negation to the number 6, we get -6. If we apply a negation to -6, we get -(-6), which is the same as positive 6.

Practice Problems

If y is true, what is y'?

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If q is true, what is q'''''?

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