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Boolean NOT
summary
This subchapter looks at Boolean NOT.
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Boolean NOT
This subchapter looks at Boolean NOT.
Please note the differences between a logical Boolean operation, an integer Boolean operation, and a bit-wise Boolean operation. Note that terminology varies, so you will eventually see references using these terms different than presented here.
In the case of a logical Boolean NOT, a TRUE is changed into a FALSE and a FALSE is changed into a TRUE. Some languages, such as C, do not have a built-in Boolean type. There are several different and incompatible encodings for TRUE and FALSE (see table below).
In the case of an integer Boolean NOT, the result is the integer one’s compliment. This works best with -1 and 0 as TURE and FALSE (or vice versa). There are several different and incompatible encodings for TRUE and FALSE (see table below).
| some languages | TRUE | FALSE | ||
|---|---|---|---|---|
| C | 1 | 0 | ||
| C | non-zero | zero | ||
| negative | zero or positive | |||
| -1 | 0 | |||
| 0 | 1 |
in the case of a bit-wise Boolean NOT, every individual bit is changed (one bits become zero bits and zero bits become one bits).
NOT
NOT (also called negation or complement) simply reverses the value of an object, changing true into false and changing false into true.
The truth table for NOT is as follows:
| A | result |
|---|---|
| 0 | 1 |
| 1 | 0 |
The NOT gate (or inverter) in logic circuits looks like:
As in ordinary algebra, in mixed expressions, all ANDs (Boolean multiplication) are performed before ORs (Boolean addition). For example, A+B·C is evaluated by ANDing B with C and then ORing A with the result of the first operation (BC).
Parenthesis can be used to change the ordinary order of evaluation. For example, (A+B)·C is evaluated by ORing A with B and then ANDing C with the result of the first operation (A+B). Parenthesis can be used for clarity.
Negation of a single variable or object is done before using the result in an expression. Negation of an entire expression is done after the expression is evaluated.
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