Logic

What to expect

The history of boolean logic and how it links to computer architecture.

Hear about George Boole but also Mary Boole, the development of the transistor and silicon logic gates, Claude Shannon and why two’s complement binary numbers are used.

An old joke about logic goes like this: A Mathematician, a Physicist, and an Astronomer were travelling north by train. They had just crossed the border into Scotland, when the Astronomer looked out of the window and saw a single black sheep in the middle of a field. “All Scottish sheep are black,” he remarked. “No, my friend,” replied the Physicist, “Some Scottish sheep are black.” At which point the Mathematician looked up from his paper and glanced out the window. After a few second’s thought he said blandly: “In Scotland, there exists at least one field, in which there exists at least one sheep, at least one side of which is black.”

TL;DR.

George Boole (1815 – 1864) wrote “Mathematical Analysis of Logic” in 1847 describing what became known as boolean algebra. Claude Shannon saw how to apply Boole’s work to electronics, publishing “A Symbolic Analysis of Relay and Switching Circuits” in 1938. The first digital computers used fragile valves and slow relays. Transistor computers arrived in the 1950s greatly improving speed and reliability.

Computers use a high voltage (around 5 volts) to represent either “True” or a binary “1” and a low voltage (close to zero volts) to represent “False” or a binary “0”. A transistor acts like an electronic switch, turning the voltage on or off in another part of the circuit. Transistors can be combined into logic gates.

A logic gate is a collection of microscopic transistors that perform a boolean logic operation such as AND, OR and NOT. Logic gates are combined into circuits inside a computer to perform arithmetic and logical operations.

References

Refs for Logic…

[110] https://www.allaboutcircuits.com/textbook/digital/chpt-3/logic-signal-voltage-levels 

[111] https://en.wikipedia.org/wiki/A_Symbolic_Analysis_of_Relay_and_Switching_Circuits

[112] https://student.craigndave.org/videos/slr-15-boolean-algebra

[113] http://the.computing.cafe/a726981f

[114] https://www.inf.ed.ac.uk/teaching/courses/inf1/cl/tools/venn/

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[115] https://www.rigb.org/christmaslectures08/html/under-the-surface.htm

[116] http://www.minecraft101.net/redstone/redstone-logic.html

[117] https://www.instructables.com/Logic-Gates-in-Minecraft/

[118] https://www.allaboutcircuits.com/projects/how-to-build-your-own-discrete-4-bit-alu/