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How to translate the number system

How to translate the number system

In information technology, we instead of the usual decimal system is often used binary, since it is based on work computers.



Basic operations are only two: translation of the decimal number system to another (binary, octal, etc.) and back. The name of each number system comes from its base - is the number of elements in it (binary - 2 decimal - 10). The radix is ​​greater than 10 made further use as a replacement for two-digit numbers of the Latin alphabet (A - 10, B - 11, etc.).


Operations by the example of the binary systemradix, as the most common. For all other systems will be true the same rules and methods to within 2 base substitutions at appropriate.
So, we have a number in binarynumber system consisting of several digits. Write it as the sum of its digits works, multiplied by 2. Then we arrange all 2 degree from right to left, starting from 0. We summarize. Get the number is required.
1011 = 1 * (2 ^ 3) + 0 * (2 ^ 2) + 1 * (2 ^ 1) + 1 * (2 ^ 0) = 8 + 0 + 2 + 1 = 11.


Now consider the inverse operation.
Given a number in the decimal system. We share his column in the radix in which we want to translate it (in our case it will be a 2). The division lasted until the very end, while private is less than the base. Further, since the last one, we write all the remains in place. This will be the required number.
11/2 = 5 remainder of 1, 5/2 = 2, remainder 1, 2/2 = 1 remainder 0 = & gt- 1011.
Another example is shown in the picture.
For other operations are similar to the grounds. Do not forget to replace the numbers, starting with 10 in the corresponding numerical systems on letters! Otherwise, the resulting number will be read incorrectly, as "10" and "1" 0 "- it is absolutely different things!
Radix, which is represented by the numbers indicated in the form of an index at the bottom of the rightmost digits of the number.

How to translate the number system

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