Because Boolean algebra came naturally to him, he marveled at how simple, rather than complex, the computers were.

在接触到布尔代数之后，他惊奇地发现其实计算机系统一点儿也不复杂，而是非常简单。

The AND Boolean operation takes two inputs, but still has a single output.

AND 布尔运算需要两个输入，但仍然只有一个输出。

Let me drag that Boolean expression into that similar shape.

让我把那个布尔表达式拖成类似的形状。

Very similar, again, to a condition with its own Boolean expression.

同样，非常类似于有自己的布尔表达式的条件。

For that we need something called Boolean expressions.

为此，我们需要一种叫做布尔表达式的东西。

This condition, though, is any Boolean expression.

不过，这个条件是任何布尔表达式。

It kind of tastes like Boolean, or, like, Cup of Noodle [beep].

它有点像布尔值，或者像 Cup of Noodle [哔哔声]。

You can have Boolean values, which are only true or false.

可以有布尔值，这些值只能是true或false。

And in boolean algebra, there are only two, binary values: true and false.

在布尔代数中，只有两个二进制值：真和假。

X less than y is my Boolean expression.

X小于y是我的布尔表达式。

For example, another useful boolean operation in computation is called an Exclusive OR - or XOR for short.

例如，计算中另一个有用的布尔运算称为异或 - 或简称 XOR。

Now here's the cool part -- we can easily build boolean logic out of transistors.

现在这是很酷的部分——我们可以轻松地用晶体管构建布尔逻辑。

And Boolean logic just refers to true or false.

布尔逻辑只是指真或假。

Before we packed up things like transistor circuits into higher-level boolean gates.

在我们将诸如晶体管电路之类的东西打包到更高级别的布尔门之前。

But in Boolean Algebra, the values of variables are true and false, and the operations are logical.

但在布尔代数中，变量的值是真假，运算是合乎逻辑的。

So, last episode we talked about how transistors can be used to build logic gates, which can evaluate boolean statements.

所以，上一集我们讨论了如何使用晶体管来构建逻辑门，逻辑门可以计算布尔语句。

A NOT takes a single boolean value, either true or false, and negates it.

NOT 接受单个布尔值（true 或 false）并将其取反。

Or in boolean terms, when the input is true, the output is true.

或者用布尔术语来说，当输入为真时，输出为真。

There are three fundamental operations in Boolean Algebra: a NOT, an AND, and an OR operation.

布尔代数中有三种基本运算：NOT、AND 和 OR 运算。

George Boole, from which Boolean Algebra later got its name, was a self-taught English mathematician in the 1800s.

布尔代数后来得名的乔治布尔是 1800 年代一位自学成才的英国数学家。