Binary system: arithmetic operations and scope

From childhood we are taught to things that we can not do without in adult life: to perform some simple actions, politely talk, read, count. Probably, everyone remembers with what difficulty he was given an account in the kindergarten or in the primary classes, how hard it was to get used to writing numbers correctly. After some time, we are so used to the fact that everything is based on the decimal system (account, money, time) that we are not even aware of the existence of other systems (also widely used in various fields of activity, for example, in manufacturing or IT ).

One of such "non-standard" variants of the numbering is the binary system. As you can see from the name, the entire set of characters in it consists of 0 and 1. Although it seems simple, but the binary system is used in the most complex technical devices today - computers and other automated systems.

The question arises: why they decided to use it, because it is much more convenient for a person to focus on the usual 10 digits? The fact is that a computer is a machine that works by electricity, and its software stuffing consists, in essence, of the simplest action algorithms. The binary system from the point of view of the computer has in comparison with others a number of advantages:

1. There are 2 states for the machine: it works or not, there is current or no current. Each of these states characterizes one of the symbols: 0 - "no", 1 - "yes".

2. The binary (binary) system makes it possible to simplify the device of microcircuits as much as possible (that is, it is enough to have two channels for different types of signals).

3. This system is more noisy and fast. It is immune to interference because it is simple, and the risk of software malfunction is minimized, but fast because binary algebra is much easier to implement than decimal.

4. Boolean operations with binary numbers are much easier to perform. In general, the logic algebra (Boolean) is designed to understand complex signal transformation processes in computer systems.

If you are studying for a technical profession, you are probably familiar with the basics of representing numbers in binary form. The usual person, inexperienced in such cases, arithmetic operations with 0 and 1 are necessary for a more complete understanding of the computer, which, certainly, everyone has.

So, with zero and one, you can perform the same arithmetic operations as with ordinary digits. In this paper, we will not consider operations such as inversion, addition modulo 2, and others (purely specific).

Consider how the addition in the binary system of numbers takes place . For example, we add two numbers: 1001 and 1110. Beginning with the last digit, add: 1 + 0 = 1, then 0 + 1 = 1, the next action: 0 + 1 = 1, and finally 1 + 1 = 10. Total we got the number 10111.

Subtraction in the binary system is based on the same principles. For example, take the same numbers, but now subtract 1001 from 1110. We also begin with the last digit: 0-1 = 1 (minus 1 from the next digit), then also on the sample. Total 101.

The division and multiplication also have no fundamental differences in comparison with the principles of the usual decimal form.

In addition to binary, the computer uses ternary, octal and hexadecimal number systems.