Name: 第一週，繼續 (Week 1, continued)
Uploaded: 2021-01-14T06:22:18.000Z
Duration: 52 min 50 s

>> DAVID J MALAN: All right, so this is CS50.

>> 大衛·馬蘭：所有 沒錯，所以這是CS50。

情態副詞

So you may recall that we left off, last time, with a cliffhanger of sorts.

所以，你可能還記得，我們​​不放過， 最後一次，有各種各樣的懸念。

Whereby we expose this lie, that no matter what you've been taught growing

我們藉以揭露這個謊言，沒有 不管你被教導成長

up, 1 divided by 10 is not, in fact, 0.1 or 0.100 or 0.10000.

向上，1除以10不是在 事實上，0.1或0.100或0.10000。

In fact, if we compile this program, as we did yesterday, with,

事實上，如果我們編譯這個 計劃，因為我們沒有昨天，有，

make imprecision, and then do dot, slash, imprecision,

使不精確性，然後 做點，斜線，不精確，

we learned that this is what's 1 divided by 10 actually is.

我們了解到，這是什麼 1除以10實際上是。

所以這不是真的相當的情況下。

But this does hint at some fundamental limitation of computers.

但是，這確實暗示了一些 電腦的基本限制。

And indeed, among the things we're going to do

today is take a look at why this has happened, what implications this has,

今天就來看看為什麼這有 事情發生了，有什麼意義這有，

how humanity has failed to grasp this in some very

serious situations-- the result of the which

has been quite tragic and expensive-- and also

take a look at how we can actually defend

So intuitively, perhaps, why is 1 divided by 10,

所以直覺，也許， 為什麼是1除以10，

according to my computer here, not just 1/10, 0.10?

根據我的電腦 這裡，不只是的1/10，0.10？

>> AUDIENCE MEMBER: The radix is different?

It's actually more fundamental to the hardware.

AUDIENCE MEMBER: They represent numbers differently?

So that is-- Well, differently from what?

They don't use the decimal system to [INAUDIBLE].

它們不使用小數 系統[聽不清]。

So in a sense, they don't use the decimal system.

因此，從某種意義上說，他們不 使用十進制系統。

Underneath the hood, everything is, indeed, binary,

在系統底層， 一切，的確，二進制，

But it's even a simpler explanation than that.

>> AUDIENCE MEMBER: They only have so many bits.

>> 觀眾：他們 只有這麼多的位。

They can only store up to a certain extent, like with the decimals.

他們最多只能存儲一定 某種程度上，像小數。

It turns out that computers typically, will always only

事實證明，計算機 通常情況下，將永遠只有

use a finite amount of information to represent something.

使用的信息的有限數量 代表什麼。

After all, we only have a fixed amount of hard disk space.

畢竟，我們只有一個固定的 量的硬盤空間。

We only have a fixed amount of RAM, or computer memory.

我們只有一個固定量 的RAM，或計算機的內存。

And if you only have a fixed amount of something,

如果你只有一個 固定金額的東西，

surely you can't actually count up to infinity or any number you want.

當然你不能真正計數 到無窮大或任何你想要的數字。

You, kind of, have to pick and choose what range

>> And so for instance, a week or two ago, when we talked about ASCII,

>> 因此，例如，一兩個星期 以前，當我們談到ASCII，

and we talked about 8 bits, or a byte, so to speak,

我們談了8位， 或字節，可以這麼說，

the biggest number we could represent with 8 bits was what?

最大數我們可以 有8位表示是什麼呢？

And we can represent 256 total values but not if we spend one of them

我們可以表示256個總價值 但如果我們把其中的一個

on 0-- Well, but if we spend one of them on 0,

在0--好了，但如果我們 花其中的一個0，

then the biggest number is, of course, 255.

>> So it turns out, that this is the case too, in this context.

>> 所以，事實證明，這是 的情況下也一樣，在這種情況下。

We started talking, last time, about floating-point numbers, which

我們開始談，最後一次， 有關浮點數字，

are different from integers, in that they have a decimal point

來自整數不同，在 他們有一個小數點

and, hopefully, some numbers after that, but they are too.

並希望一些數字 在這之後，但是它們太。

A computer is only typically going to use 32 bits, maybe 64 bits

一台計算機通常只打算 使用32位，也許64位

So even though we've grown up learning mathematics and knowing

因此，即使我們已經長大了 學習數學和了解

that you can absolutely have an infinite number of numbers

after the decimal point, not if you have finite memory.

小數點後不 如果你有有限的內存。

You, kind of, have to round, or pick and choose which

你有種，有圓形， 或者挑選哪些

And so you can think of, in a sense, this being the computer's closest

所以，你能想到的，從某種意義上說， 這是計算機的最接近

approximation to the value 1/10 that it can get, with just 32 or so bits.

近似​​的值的1/10 它可以得到，只有32左右位。

>> For instance, if I change this to 1/3, which we think is even simpler.

>> 舉例來說，如果我改變這 1/3，我們認為這是更簡單。

Here too, apparently, 1/3 is not 0.3 and then an infinite number of 3's

在這裡，顯然，三分之一沒有0.3 然後3的無限數量

So we humans are correct, and what you learned is, in fact, correct,

所以，我們人類是正確的，什麼 你了解，其實，正確的，

but we're bumping up against some limitations.

>> And what I thought we'd do today, is begin

>> 而我的想法 我們今天會做，是開始

by looking at, frankly, the tragic consequences of this

通過看，坦率地說，在 這種悲慘的後果

sometimes, when mankind does not quite implement

有時，人類的時候 並不完全實現

And we'll see a series of vignettes from the History Channel that takes

而且我們會看到一系列的小插圖 從歷史頻道的需要

一起來看看如何事情已經出了問題。

It's about 8 minutes long, and we'll come back after this

這是約8分鐘之久， 我們將在這之後回來

and take a look at exactly what else can go wrong.

看一看在完全相同 還有什麼可能出錯。

>> -Computers, we've all come to accept the often frustrating problems that

>> -Computers，我們都逐漸接受 經常令人沮喪的問題，

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第一週，繼續 (Week 1, continued)

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