Introduction To Boolean
In 1854, George Boole performed an investigation
into the “laws of thought” which were based on a simplified version of
the “group” or “set” theory, and from this Boolean or “Switching” algebra was developed. Boolean Algebra deals mainly with the theory that both logic and set operations are either “TRUE” or “FALSE” but not both at the same time.
For example, A + A = A and not 2A as it would be in normal algebra. Boolean Algebra
is a simple and effective way of representing the switching action of
standard Logic Gates and the basic logic statements which concern us
here are given by the logic gate operations of the AND, the OR and the NOT gate functions.The logic AND Function
The Logic AND Function function states that two or more events must occur together and at the same time for an output action to occur. The order in which these actions occur is unimportant as it does not affect the final result. For example, A & B = B & A. In Boolean algebra the Logic AND Function follows the Commutative Law which allows a change in position of either variable.The AND function is represented in electronics by the dot or full stop symbol ( . ) Thus a 2-input (A B) AND Gate has an output term represented by the Boolean expression A.B or just AB.
Switch Representation of the AND Function
Then this type of logic gate ( an AND Gate ) only produces an output when “ALL” of its inputs are present. In Boolean Algebra terms the output will be TRUE only when all of its inputs are TRUE. In electrical terms, the logic AND function is equal to a series circuit as shown above.
As there are only two Switches, each with two possible states “open” or “closed”. Defining a Logic “0” as being when the switch is open and a Logic “1” when the switch is closed, there are then four different ways or combinations of arranging the two switches together as shown.
AND Function Truth Table
| Switch A | Switch B | Output | Description |
| 0 | 0 | 0 | A and B are both open, lamp OFF |
| 0 | 1 | 0 | A is open and B is closed, lamp OFF |
| 1 | 0 | 0 | A is closed and B is open, lamp OFF |
| 1 | 1 | 1 | A is closed and B is closed, lamp ON |
| Boolean Expression (A AND B) | A . B | ||
