- The system of logic that is the basis for modern computing.
An englishman born in Lincoln, George Boole developed his ideas of logic and algebra as the first Professor of Mathematics at the University of Cork in the mid 18th century. A largely self taught prodigy he was influenced by religion and mystical ideas, claiming to have had a revelation as a young man which initially inspired him to join the church, in fact though he went on to dedicate his life to academic study. He become the first to build on Leibniz’s ideas successfully combining the the philosophical field of logic and mathematical algebra. He fathered several daughters who were notable in their own right including Lucy Everest, the first female professor of chemistry in England.
The impact of Boole’s ideas was wide ranging, but the key development that was crucial for the development some years later of computing (and therefore digital cinematography) is two-element Boolean algebra, often known as “switching algebra”.
Switching algebra uses simple logic operations as its building blocks. These logic operations operate on BITS and can be replicated by simple mechanisms or circuits utilising vacuum tubes or transistors. It is arrays of millions of tiny transistors performing logic operations sequentially that constitute the silicon chip. When combined appropriately these logic operations can mimic the the most complex mathematical functions. Boole’s algebra, later perfected by Claude Shannon (an electronic engineer and mathematician whose work at MIT was initially aimed at telephonic switching, but whose thesis became the basis of wartime cryptography and modern computing, and is sometimes hailed as the most important scientific paper of all time!) Using Boolean algebra to efficiently combine simple logic operations into circuits performing complex functions is the main challenge of the circuit engineer today.
The three basic logic operations that form the basis of switching algebra are as follows:
The NOT gate:
- one input, one output, the output is the opposite of the input.
The AND gate:
- two inputs, one output, the output is 1 if both one input AND the other input is 1
The OR gate:
- two inputs, one output, the output is 1 if one input OR the other input is 1
Other commonly used but basic operations NAND, NOR, XAND and XOR can be made by combining these three most basic operations.