The mathematician and philosopher George Boole (1815–1864) developed the association between logic and mathematics by analyzing the laws of mental operations underlying reasoning, and expressing them in a symbolic language that would allow logical operators to act like algebraic operators, by means of computable statements. He created what is known as Boolean algebra.
Boolean logic is the foundation of computer science and digital electronics, and it is based on the manipulation of variables that can take only two values: True (1) and False (0). The Boolean logical operators, detailed below, are applied as ‘logic gates’ in electronic devices, making it possible to build the basic operations, then replicated billions of times in modern devices, to create the computers and smartphones we know. More precisely, these include both physical gates, transistors* in hardware, and non-physical gates, in the instructions of operating system and application code.
The fundamental operators are:
AND: returns true (1) only if all inputs are true.
OR: returns true (1) if at least one input is true.
NOT (negation): an operator that inverts the input value: 1 becomes 0, and vice versa.
| A | B | AND (A*B) | OR (A+B) |
|---|---|---|---|
| 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 1 |
| 1 | 0 | 0 | 1 |
| 1 | 1 | 1 | 1 |
Using the fundamental operators one can build the logic gates:
NAND (Not-AND): output is false only if all inputs are true.
NOR (Not-OR): output is true only if all inputs are false.
XOR (Exclusive OR): true if the inputs are different, false if they are the same.
Combinations of these gates and the fundamental operators, together with an algebra that makes them workable, make it possible to build digital circuits and instruction structures that process and store data.
Transistor*
Transistors are devices made of semiconductor materials (e.g., modified silicon) that behave like a ‘switch’, regulating current flow on the basis of a control signal (in the sense that its value determines whether the flow can pass or not).
OFF state: if there is no signal on the control (value 0), the transistor blocks the flow (open circuit).
ON state: if there is a signal on the control (value 1), the transistor allows the flow (closed circuit).Logic gates can thus be built:
AND gate: two transistors in series; current flows only if both are ON (1 AND 1 = 1)
OR gate: two transistors in parallel; current flows if at least one of the two is ON (1 OR 0 = 1)
NOT gate: called an inverter; a single transistor configured so as to disconnect the output (open circuit) if it receives the signal (value 1).
