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如何能通过加法来做减法 – 译学馆
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如何能通过加法来做减法

How to Subtract By Adding

假设你想知道多长时间是诺曼人入侵英格兰和哥伦布的之间
Suppose you want to know how long it was between the Norman invasion of England and Columbus’s
到达加勒比海;也就是说,1492年代 – 1066年代,但是你讨厌长减法
arrival in the Caribbean; that is, what’s 1492 minus 1066 – but you hate long subtraction
借位之类的东西。
with its borrowing and such.
我们可以减去通过添加:首先我们只需要替换小的每一位
Well, we can subtract by adding: first we just need to replace each digit of the smaller
数量与9 -位,除了最后一个数字被替换为10 –
number with 9 minus that digit, except the final digit gets replaced with 10 minus that
数字,所以1066 9 – 1、9 – 0、9 – 6、10 – 6。加到
digit, so 1066 becomes nine minus 1, nine minus 0, nine minus six, ten minus 6. Adding
1492上得到10426,如果我们忽略第一位数,我们得到答案:1492 –
that to 1492 gives 10426, and if we ignore the first digit, we get the answer: 1492 minus
1066年是426。您可以检查来确定。巧合的是,它约为426倍
1066 is 426. You can check just to be sure. Coincidentally, it’s roughly 426 times farther
从葡萄牙和西印度群岛比从法国到英国更远。
from Portugal to the West Indies and back than from France to England.
但无论如何,用加法做减法技巧适用于任何正数!8 – 6,
But anyway, the subtraction-by-adding trick works for any positive numbers! 8 minus 6,
或2,是一样的8 + 4,忽略第一个数字。
or 2, is the same as 8 plus 4, ignoring the first digit.
100 – 1 ?是100 + 999,也就是99年,忽略第一个数字。
100 minus 1? is 100 plus 999, which is 99, ignoring the first digit.
424242 – 333333 = 424242 + 666667,或90909,忽略第一个数字。
And 424,242 minus 333,333 is 424,242 plus 666,667, or, 90,909 ignoring the first digit.
我会让你检查的。
I’ll let you check that one.
这个技巧似乎是无用的,但假设你建立了一个机器,可以把数字加起来,
This trick might seem useless, but suppose you built a machine that can add numbers together,
你想让它减去吗?在这种情况下它可能会更容易用加法作减法
and you wanted to make it subtract? Well, in that case it might be easier to make it
事实上,我朋友(汉克•格林)拆开一个加法机器
subtract by adding: and matter of fact, my friend Hank Green took apart an adding machine
那正是它如何作减法的,通过加法!
and that’s exactly how it subtracts – by adding!
基本上机器通过转动数字轮来做加法
Basically, the machine adds numbers by rotating numbered wheels, but there aren’t infinitely
但是没有无限多的轮子 所以当你加过最大可能数字时 你得到的数又回到零
many wheels so if you add up past the maximum possible number, you get back to zero – this
这在计算中被称为“溢出” 在数学中被称为模算术
is called “overflow” in computing and “modular arithmetic” in mathematics. But
但最重要的是 通过加法得到的数字回到零意味着
most importantly, getting back to zero by adding means it’s possible to have positive
可以得到正负数 例如既然-3只是加上三得到零
negative numbers, since, for example, negative three is just what you add to three to get
而在汉克的加法机器中 如果你让三加上9997.00 你得到了零
zero, and on Hank’s adding machine if you add 3 plus 9,997.00, you get zero, so 9,997
所以9997实际上是-3
is literally negative three!
不幸的是 当你在做正常的算数时有无穷的数字
Unfortunately, there are an infinite number of numbers when you’re doing regular arithmetic,
所以你会认为-3只是-3
so you might think that negative three is just negative three. But if you’re willing
但如果你愿意蒙混过关时 你可以选用加法机器式的-3
to fudge a little, you can just take the adding machine’s version of negative three, add
在前面加上一串九 而当你在前面加上那东西时那基本上就
a bunch of 9s out in front, and when you add that to stuff it’s BASICALLY the same as
等同于减去三 只要你看得没那么远 因为 你知道
subtracting three, as long as you don’t look too far. Because, you know, nine gadgillion
九亿九千九百九十七加上三是零 基本上
nine hundred and ninety bajillion nine hundred and ninety seven plus three, is zero. Almost.
顺便说一下这种用减法做加法的方法也是计算机做减法的方式
By the way, this method of subtracting by adding is how computers subtract as well,
他们用二进制计算所以简单得多
they just do it in binary which makes it a lot easier. It’s called "subtracting using
这叫做“使用二进制补码做减法”
the two’s complement," if you want to
如果你想查字典的话
look it up.

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