Let's talk about number systems. Scheme, description

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ENCYCLOPEDIA OF RADIO ELECTRONICS AND ELECTRICAL ENGINEERING
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Let's talk about number systems. Encyclopedia of radio electronics and electrical engineering

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Encyclopedia of radio electronics and electrical engineering / Beginner radio amateur

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The number system, which we are all accustomed to from the cradle, is decimal. Ours, dear!

We think so:

0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18… etc.

However, this is why the dense science of Mathematics exists in nature, to periodically spoil the whole thrill of life for us. Here we go again... In short, in addition to the painfully familiar decimal number system, it turns out that there are all sorts of different systems. Well, how can you continue to live here when faith in the indestructible is destroyed!..

However, we will live. But first we need to get to know each other better...

So, there are many different number systems. Let's choose the one that is most important to us (after the decimal, of course). Well of course it is binary ss!

Well, firstly, what is "decimal", "binary", etc.? The name of the s.s. tells us what she has base.

The base is the number of values that one bit of a number in a given s.s. can take. In other words, how many numbers can be written using one character.

For decimal s.s. - base = 10 (from 0 to 9, total - 10 values).

В binary s.s - base = 2 (0 or 1, total - 2 values).

In the decimal system, after the values at the current bit depth are exhausted, one more significant digit is added. After 9 comes 10, after 99 comes 100, etc.

In binary s.s. - same. Here's how we'll count up to 10 in binary s.s.:

Decimal	Binary
0	0
1	1
2	10
3	11
4	100
5	101
6	110
7	111
8	1000
9	1001
10	1010

0 is 0

1 is 1.

That's it, the values of 1-bit numbers are exhausted. Add a new digit to the left:

Again the values are exhausted. We write another category:

100

101

110

111

And so on…

Now that we understand the principle of forming binary numbers, it will be easy for you to continue counting beyond ten. First, count how old you are today in binary.

Have you counted? Happened? Long steamed???

And now translate to me in binary code, say, the number 167 :)!

Aha! Difficult? Well, yes, who wants to count up to 167, especially in the binary system! So, we need to learn how to somehow translate binary values into decimal ones with less blood.

Publication: radiokot.ru

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