Although recording methods have changed, the decimal system has triumphed throughout.

虽然记录方法发化，十进位制在整个过程中都占着主导地位。

Or in a given row, treat each number as part of a decimal expansion.

或是将其中一列作十进位展开。

Using binary code — the base two numbering system that only uses 1s and 0s — we can represent each of the 4 disks with a 2-bit binary number

使用二元码，也就是只用 1 和 0 的二进位数字系统，我们可以用两位元的二元数字来别代表这四个硬碟：从代表 0 的 00 到代表 3 的 11。

The base 12 system coming from the fact that there are roughly 12 hours of daylight and 12 hours of darkness during each observed equinox.

以 12 为进位基数的系统来源于这样一个事实，即在每个观测到的昼夜平点，大约有 12 小时的白昼和 12 小时的黑夜。

Right, the Dewey decimal classification system which was invented by Melville Dewey, an American librarian, not John Dewey, the philosopher.

杜威十进位类法是由梅尔维尔·杜威发明的，他是一位美国图书管理员，而不是哲学家约翰·杜威。

Turning switch 11 on gives us 110 by standard binary addition.

根据标准二元进位法，如果打开 11，我们会得到 110。

Each bit can be either a zero or a one in the binary language of computing.

在计算机的二进位语言中，每个比特代表0或1。

And 60 originating from, well, I don't really know, but it does divide pretty nicely with smaller numbers such as 10 12 15 20 and 30 which may be why it was originally chosen.

以 60 为进位基数的系统来自，嗯，我不太，它确实能与较小的数字如 10，12，15，20 和 30 除开，这可能是它最初被选择的原因。

Ancient civilizations such as the Egyptians and the Greeks first divided the day into smaller parts based on a base 12 and base 60 system that we continue to use to this day.

古代文明，如埃及人和希腊人，首先根据 12 进位和 60 进位的系统将一天成更小的部，我们一直沿用至今。

So we have 2.0, and then in the next digit you go up here.

所以我们有2.0，然后在下一位数字上向上进位。

I think that's what's nice is this was not dependent on 20 carries.

我认为这很好，因为这不依赖于 20 个进位。

As a math person, I prefer to think about it as addition mod 2. We also commonly talk about the xor of two different bit strings, which basically does this component-by-component; it's like addition but where you never carry.

作为一个数学人士， 我更倾向于将其视为模2加法。 我们通常也会讨论两个不同比特串的异或操作，这基本上是对每个位进行这样的操作；它类似于加法， 不会进位。

Things that aren't necessarily there, or if you do turn up a discrepancy, assuming that it does reveal some larger plot rather than just being a mistake or an accounting error or somebody forgot to carry the one.

一些不一定存在的东西，或者如果你确实发现差异，假设这揭示一些更大的阴谋而不是仅仅是一个错误或记账失误或有人忘记进位。

It's possible there was a carry from the previous addition of A0 and B0, so this time we need to use a full adder that also inputs the carry bit. We output this result as sum1.

有可能之前A0和B0的加法有进位，所以这次我们需要使用全加器，也输入进位位。我们将此结果输出为 sum1。

You might be used to working from the smallest number to the largest, carrying ones as needed, but that can be pretty tricky to keep track of in your head.

你可能习惯于从最小的数字开始加到最大的数字，需要进位一， 这在心里记起来可能会相当棘手。

Let's do it with an algorithm that you probably learned in first grade, addition, where you loop over the digits from right to left, and sometimes you do a carry.

让我们用一个你可能在一年级学过的算法来做这件事，那就是加法， 你从右到左逐位相加，有时还需要进位。

If there is a carry into the 9th bit, it means the sum of the two numbers is too large to fit into 8-bits.

如果第9位有进位，这意味着两个数字的和太大，无法放入8位中。

Well, they don't do carrying over like we used to do.

现在算进位的方法已经跟我们当年不一样。

And when any place fills up with ten, we just roll it over to the next highest place.

当任何一个位置填满十，我们就将其进位到下一个更高的位置。

Notice how our last full adder has a carry out.

注意我们的最后一个全加器有一个进位输出。