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How to translate the number system


How to translate the number system

In information technology, instead of the usual decimal number system, binary is often used, as the work of computers is built on it.



The main operations are only two: Translation from decimal to another (binary, octal, etc.) and vice versa. The name of each number system comes from its base - the number of elements in it (binary - 2, decimal - 10). In base systems with a base greater than 10, it is customary to use the letters of the Latin alphabet (A-10, B-11, etc.) as a replacement for two-digit numbers.


Let's consider the operations using the example of a binary systemNumbering, as the most common. For all other systems, the same rules and methods will be true to the replacement of base 2 by the corresponding one.
So, we have some number in binaryNumber system consisting of several digits. We write it in the form of the sum of the products of its digits multiplied by 2. Next, we arrange all the powers from right to left starting from 0. We sum up. The resulting number is the required number.
1011 = 1 * (2 ^ 3) + 0 * (2 ^ 2) + 1 * (2 ^ 1) + 1 * (2 ^ 0) = 8 + 0 + 2 + 1 = 11.


Now consider the reverse operation.
Let there be given a number in the decimal system. We will divide it by a column on the basis of the number system into which we want to translate it (in our case this will be 2). The division continues to the very end, until the private becomes less than the ground. Next, starting with the last, we write down all the remains in the line. This is the required number.
11/2 = 5 the rest is 1, 5/2 = 2, the rest is 1, 2/2 = 1 the remainder is 0 = & gt- 1011.
Another example is shown in the picture.
For other bases, operations are similar. Do not forget to replace the numbers, beginning with 10, in the corresponding number systems in Latin letters! Otherwise, the resulting number will be read incorrectly, because "10" and "1" 0 "are absolutely different things!
The base of the number system, in which the number is represented, is indicated in the form of an index at the bottom of the rightmost digit of the number.

How to translate the number system

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