The Physics Department at Princeton had a small but well equipped machine shop for its graduate students to use,
普林斯顿的物理系有一个很小、但是很不错的机械加工间，供研究生使用。
and my small contribution to the project was to lend Turing my key to the shop, which was probably against all the regulations,
我对这个计划的小贡献就是，把我的钥匙借给了图灵，这可能是违反规定的。
and show him how to use the lathe, drill, press etc.without chopping off his fingers.
我还教他使用车床，钻机，冲压等等，我告诉他怎么操作才不会切断手指。
And so, he machined and wound the relays; and to our surprise and delight the calculator worked.
他最终成功地做出了继电器，他的乘法机很好用，我们很高兴。
Mathematically, this project was not advanced, for it used only multiplication.
从数学的角度看，这个项目并不高级，因为它只能计算乘法。
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，尽管它没有应用什么高级理论，但它体现出来的某些基础数学的应用价值，是1937年的人们没有发现的。
For one thing, the binary representation of numbers would have seemed a novelty to anyone then engaged in practical computations.
首先，用二进制形式进行实际计算，这看起来很新奇。
Alan had used binary numbers in Computable Numbers.
艾伦在《可计算数》中已经使用了二进制，
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就能表示所有的可计算数。
In a practical multiplier, however, the advantage of binary numbers was more concrete: it was that the multiplication table then reduced to:
在实际的乘法机中，二进制的优势更加明显，它使乘法简化为：
The binary multiplication table being so trivial, the work of a multiplier would be reduced to carrying and adding operations.
二进制的乘法表是非常简洁的，乘法机要做的只是移动和相加。