A second aspect of his project was its connection with elementary logic.
这项计划的第二点是关于逻辑，
The arithmetical operations with 0s and 1s could be thought of in terms of the logic of propositions.
对0和1进行的算术运算，可以看作是逻辑运算，
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，可以看成等价于逻辑上的"与"运算。
For if p and q were propositions, then the following 'truth-table' would show in what circumstances 'p AND q' was true:
也就是说，如果有命题p和q，则p与q的真值表可以表示为：
It was the same game, with a different interpretation.
这是同样的运算，只是解释不同。
All of this would have been entirely familiar to Alan, the calculus of propositions appearing on the first page of any text on logic.
艾伦对这些东西非常熟悉，任何一本逻辑教材的第一页都会讲这些运算。
It was sometimes called 'Boolean Algebra' after George Boole, who had formalised what he optimistically called 'the laws of thought' in 1854.
1854年，乔治·布尔将他所说的思考规则形式化，从那以后，这些运算有时也被称为布尔代数。
Binary arithmetic could all be expressed in terms of Boolean algebra, using AND, OR, and NOT.
所有的二进制运算都可以用与，或，非来表示成布尔代数。
His problem in designing the multiplier would be to use Boolean algebra to minimise the number of these elementary operations required.
艾伦在设计乘法机时，就通过布尔代数来减少需要的基本操作的数量。
This, as a paper exercise, would be very similar to that of designing a 'Turing machine' for the same problem.
这个方法，也同样可以用来制造图灵机。