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In a minute: Boolean algebra + Simplifying circuits

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Boolean algebra
https://plus.maths.org/content/maths-min...an-algebra

EXCERPT: Every time you use a computer you are relying on Boolean logic: a system of logic established long before computers were around, named after the English mathematician George Boole (1815 - 1864). In Boolean logic statements can either be true or false (e.g. at the moment "I want a cup of tea" is false, but "I want a piece of cake" is always true), and you can string these together using the words AND, OR and NOT. To establish if these compound statements are true of false, you might create what's called a truth table, listing all the possible values the basic statements can take, and then all the corresponding values the compound statement can take. Truth tables are useful for simple logic statements, but quickly become tiresome and error prone for more complicated statements. Boole came to the rescue by ingeniously recognising that binary logical operations behaved in a way that's strikingly similar to our normal arithmetic operations, with a few twists....



Simplifying circuits
https://plus.maths.org/content/maths-min...g-circuits

EXCERPT: Most of us are aware that the work done by our computers is accomplished by breaking tasks down into a series of just a few logical operations. These operations – AND, OR and NOT – can be physically represented in the computer circuits and mathematically representation using Boolean algebra. This realisation of the links between circuitry, logic and algebra was first made by Claude Shannon (1916 - 2001), who in 1936 was a 20-year-old student at Massachusetts Institute of Technology writing his Masters thesis....
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