Boolean logic is named after the British mathematician and computer science pioneer, George Boole. He is best known for his work on Boolean logic – a concept that is very important in computing.
In the new discipline he developed, known as Boolean algebra, all objects are divided into separate classes, each with a given property; each class may be described in terms of the presence or absence of the same property. An electrical circuit, for example, is either on or off. Boolean algebra has been applied in the design of binary computer circuits and telephone switching equipment. These devices make use of Boole’s two-valued system.
Boolean logic
A computer is basically a collection of transistors and circuits. These components have two states:
on - a current is flowing through the component off - a current is not flowing through the component These two states can easily be represented by using binary:
1 = on (TRUE)
0 = off (FALSE)
Boolean logic can be used to check if the values of different states are the same or different when compared. When George Boole was studying mathematical theories, he discovered a relationship between algebra and logic. This led to the idea that by comparing different states using three main conditions, this would always output a true or false value. This later became known as a Boolean data type.
The three main types of condition are:
- AND
- OR
- NOT
Logic gates
Many electronic circuits have to make decisions. They look at two or more inputs and use these to determine the outputs from the circuit. The process of doing this uses electronic logic, which is based on digital switches called gates.
Logic gates allow an electronic system to make a decision based on a number of its inputs. Each input and output of the gates must be one of two state, true or false A single digital signal can be either on or off – for example, a light with one switch can be on or off.
The most common operators are operators are AND, OR and NOT (always in capitals). Each operator has a standard symbol that can be used when drawing logic gate circuits.
The NOT gate
A NOT gate has just one input. The output of the circuit will be the opposite of the input. If 0 is input, then the output is 1. If 1 is input, then 0 is output.
For example if switches are connected to NOT gates which mean we get an opposite result to the input in each case. When the switch is off (0), the light bulb is on (1). When the switch is on (1), the light bulb is off (0).
AND gate
An AND gate can be used on a gate with two inputs. AND tells us that both inputs have to be 1 in order for the output to be 1.
for example, if two switches are connected to AND gates. In order for the light bulb to be on (1), we need both switches to be on (1).
OR gate
The OR gate has two inputs. One or both inputs must be 1 to output 1, otherwise it outputs 0.
for example, if we have two switches connected to OR gates. We only need one of the two switches to be on (1) in order for the light bulb to be on (1).