A small addendum to this because there are a few cases where you have to tweak either the inputs or the output to get the answer you want.

Radix complement addition works by overflowing the "buffer" defined by the length or number of digits in the inputs. For computers, this is already a given because integer sizes are defined!

For us working on paper or tablet, we have to artificially define our buffer size.

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Alan Turing Memorial

https://en.wikipedia.org/wiki/Alan_Turing_Memorial?wprov=sfla1

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'THE IMITATION GAME' movie is about his life during WWII

"During World War II, the English mathematical genius Alan Turing tries to crack the German Enigma code with help from fellow mathematicians while attempting to come to terms with his troubled private life."

https://en.wikipedia.org/wiki/Alan_Turing?wprov=sfla1

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Alan Turing was a British mathematician, computer scientist, and logician who is widely considered to be one of the most influential figures in the history of computing. In 1936, he published a paper that introduced the concept of a universal Turing machine, which is a theoretical machine that can perform any computation that any other computing machine can perform. This concept laid the foundation for modern computer science and the development of electronic computers. During World War II, Turing worked at Bletchley Park, where he helped crack German codes using the Enigma machine. This work is estimated to have shortened the war in Europe by at least two years and saved countless lives. After the war, Turing continued to work on the development of electronic computers and contributed to the field of artificial intelligence.

Despite his significant contributions to science and technology, Turing faced significant personal troubles. In 1952, he was convicted of homosexuality, which was illegal in the UK at the time. He was given the choice of imprisonment or chemical castration, and he chose the latter. The hormone treatments that Turing received had severe side effects and caused him great distress. In 1954, Turing died by suicide at the age of 41. It wasn't until decades later that his contributions were widely recognized and he was posthumously pardoned for his conviction. Turing's life and legacy continue to inspire generations of scientists and computer scientists, and his contributions have had a profound impact on modern society.

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