雙語暢銷書《艾倫圖靈傳》第4章:彼岸新星(58)

A second aspect of his project was its connection with elementary logic.

這項計劃的第二點是關於邏輯，

The arithmeticAl operations with 0s and 1s could be thought of in terms of the logic of propositions.

對0和1進行的算術運算，可以看作是邏輯運算，

Thus the trivial multiplication table, for instance, could be considered as equivalent to the function of the word AND in logic.

比如前面的乘法表，可以看成等價於邏輯上的"與"運算。

For if p and q were propositions, then the following 'truth-table' would show in what circumstances 'p AND q' was true:

也就是說，如果有命題p和q，則p與q的真值表可以表示爲：

It was the same game, with a different interpretation.

這是同樣的運算，只是解釋不同。

All of this would have been entirely familiar to Alan, the calculus of propositions appearing on the first page of any text on logic.

艾倫對這些東西非常熟悉，任何一本邏輯教材的第一頁都會講這些運算。

It was sometimes called 'Boolean Algebra' after George Boole, who had formalised what he optimistically called 'the laws of thought' in 1854.

1854年，喬治·布爾將他所說的思考規則形式化，從那以後，這些運算有時也被稱爲布爾代數。

Binary arithmetic could all be expressed in terms of Boolean algebra, using AND, OR, and NOT.

所有的二進制運算都可以用與，或，非來表示成布爾代數。

His problem in designing the multiplier would be to use Boolean algebra to minimise the number of these elementary operations required.

艾倫在設計乘法機時，就通過布爾代數來減少需要的基本操作的數量。

This, as a paper exercise, would be very similar to that of designing a 'Turing machine' for the same problem.

這個方法，也同樣可以用來製造圖靈機。