"Pohl, Frederik - How To Count On Your Fingers" - читать интересную книгу автора (Pohl Frederick)

1 X 10^3 = 1000
9 X 10^2 = 900
5 X 10^1 = 50
6 x 10^0 = 6
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1956

(In case it has been a long time since you went to high school, 10^1 just means 10; 10^0 means ten divided by ten, or 1. No matter how long it has been since you went to high school, you ought to remember that 10^2 means ten times ten, or a hundred, and so on.)

It has been said in many science-fiction stories (and not very often anywhere else) that this is homo sapiens' "natural" system of counting, because, look, don't we have ten fingers on our hands? As a theory, let's not worry ourselves about this too much; if true, it will have plenty of chance to prove itself when our exploring rockets turn up some 12-digited and duo decimal extraterrestrials. (Or, alternatively; when our archaeologists discover that the Babylonians had six times as many fingers as the rest of us.) Still, if we assume the fable is true, we can conveniently "explain" UNIVAC by saying that the computer, not having ten fingers to count on, has to use a simpler system. The name of this simpler system is the "binary" or "dyadic" system, and it is this system that most of the world's numbers are being translated into now, in order to be taped and fed into computers.
The binary system obeys all the laws of the decimal. It is positional; it can represent any finite number; it can be used for addition, subtraction, multiplication, division, exponential functions, and any other arithmetical process known to man or to UNIVAC. The only difference is that it is to the base 2 instead of the base 10. It lops off eight of the ten basic decimal digits-0, 1, 2, 3, 4, 5, 6, 7, 8, and 9-retaining only 0 and 1.
You can count with it, of course. 1 is one; 10 is two; 11 is three; 100 is four; 101 is five; 110 is six; 111 is seven; 1000 is eight; 1001 is nine; 1010 is ten, and so on. You can subtract or add with it:
Four 100
Plus three 11
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Is seven 111

You can multiply or divide with it:
Six 110
Divided by three 11
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Is two 10

And you can do all of these things rather simply, without the necessity of memorizing multiplication tables, thus freeing your preadolescent evenings for baseball and doorbell-ringing.

Look back at Ivan's system of Russian multiplication; let us do it over again in a slightly different way. Let's halve both columns, the right as well as the left. And instead of striking out any number, let us write a "1" next to the odd numbers and a "0" next to the even ones. As follows:
87 1 93 1
43 1 46 0
21 1 23 1
10 0 11 1
5 1 5 1
2 0 2 0
1 1 1 1


Now, you might not know what you have just accomplished- and Ivan certainly wouldn't-but you have translated two decimal numbers into their binary equivalents. Reading from bottom to top, 1010111 is binary for 87; 1011101 is binary for 93.
To see what these mean, remember how we dissected a decimal number. A binary number comes apart in the same sort of pieces; the only difference is that the pieces are multiples of powers of 2, not of powers of 10. 1010111, then, is a shorthand way of saying:
1 x 2^6 = 64
0 x 2^5 = 0
1 x 2^4 = 16
0 x 2^3 = 0
1 x 2^2 = 4
1 x 2^1 = 2
1 x 2^0 = 1
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87

which is what we said it was in the first place.

When you feed numbers like 87 and 93 into UNIVAC, its digestion gets upset-in fact, it won't accept them until they are predigested. So you must convert them into binary digits ("bidgets" or "bits"), just as we did above. Such binary numbers as 1010111 and 1011101 UNIVAC handles very well indeed. Multiply them? No trouble at all. UNIVAC, in its electronic way, does something like this: