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COMPUTING THEORY – 8. Boolean logic

What is Boolean?

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.

Booleans are often used in programming and in Internet search engines. Boolean expressions result in just two values – TRUE or FALSE.

george_boole

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 states:

  • true or 1 or ‘on’
  • false or 0 or ‘off’

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

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.

Take a look at the example below. 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).

NOT

The AND gateAND_gate_3

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.

Take a look at the example below. This time 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).

AND

The OR gateOR_gate_1

The OR gate has two inputs. One or both inputs must be 1 to output 1, otherwise it outputs 0.

In the example below, 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).

OR

 

Follow this hyperlink to learn more:-

  1. BBC Bitesize

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