As first realized, computers were power-hungry, noisy contraptions of clacking gears for performing analog operations, and electromechanical relays capable of cascading digital on-off (true-false) states. Pneumatic and hydraulic computing mechanisms were also proposed. First vacuum tubes and then solid-state devices made computers a practical reality.
The initial inspiration for electronic computers was George Boole’s works including his Laws of Thought. He was an advanced mathematician who lived in England from 1815 to 1864, expiring at the age of 47 from pneumonia contracted after walking to a lecture hall in a drenching December rain.
The basic idea underlying Boolean algebra is that Boolean variables pertain to true and false, as opposed to the set of all numbers. True and false are usually represented as 1 and 0. But these symbols have nothing to do with mathematical quantities and the conventional operations known as addition and multiplication nor with their inverses, subtraction and division. Instead, there are three Boolean operations, AND (the conjunction), OR (the disjunction) and NOT (the negation), plus their derivatives.
Boolean algebra is applicable to digital electronics because the 1 and 0 can be conveyed within, between, or among components by any two agreed-upon voltage levels, such as +12 and 0, or +9 and +5. A logic gate may be either the concept or an actual device that conforms to one of the Boolean functions.
Logic gates are combined to make logic circuits. The output of an AND gate is high only when all of its inputs are high. The output of an OR gate is high only when one or more of its inputs are high. The output of a NOT gate is high only when the input is low, and it is low only when the input is high. The output of a NAND gate is high only when any of the inputs are low. The output of a NOR gate is low only when any of the inputs are high. The output of an XNOR gate is low only when either but not both of the inputs is high.
Logic gates have a single output because in our setting there can be only one output resulting from a given set of inputs. This ignores quantum effects, which are a whole different matter. Logic gates may have one or more inputs.
Integrated circuits are routinely designed using hundreds of millions of logic gates. At first they were bipolar junction transistors, then FETs and MOSFETs. The current implementation of choice is CMOS technology because with much reduced power dissipation and accompanying temperature rise, astronomical integration has become feasible.
Many researchers have concluded that the human brain is composed of a vast array of logic gates, of which consciousness is an epiphenomenon.
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