雙語暢銷書《艾倫圖靈傳》第4章:彼岸新星(57)
The Physics Department at Princeton had a small but well equipped machine shop for its graduate students to use,
and my small contribution to the project was to lend Turing my key to the shop, which was probably against all the regulations,
我對這個計劃的小貢獻就是，把我的鑰匙借給了圖靈，這可能是違反規定的。and show him how to use the lathe, drill, press out chopping off his fingers.
我還教他使用車牀，鑽機，衝壓等等，我告訴他怎麼操作纔不會切斷手指。
And so, he machined and wound the relays; and to our surprise and delight the calculator worked.
他最終成功地做出了繼電器，他的乘法機很好用，我們很高興。Mathematically, this project was not advanced, for it used only multiplication.
從數學的角度看，這個項目並不高級，因爲它只能計算乘法。But although it used no advanced theory, it involved applications of 'dull and elementary' mathematics which were by no means well known in 1937.
但是，儘管它沒有應用什麼高級理論，但它體現出來的某些基礎數學的應用價值，是1937年的人們沒有發現的。For one thing, the binary representation of numbers would have seemed a novelty to anyone then engaged in practical computations.
首先，用二進制形式進行實際計算，這看起來很新奇。Alan had used binary numbers in Computable Numbers.
艾倫在《可計算數》中已經使用了二進制，There they brought in no point of principle, but made it possible to represent all the computable numbers as infinite sequences of 0s and 1s alone.
以便只用0和1就能表示所有的可計算數。In a practical multiplier, however, the advantage of binary numbers was more concrete: it was that the multiplication table then reduced to:
在實際的乘法機中，二進制的優勢更加明顯，它使乘法簡化爲：The binary multiplication table being so trivial, the work of a multiplier would be reduced to carrying and adding operations.
二進制的乘法表是非常簡潔的，乘法機要做的只是移動和相加。
