bázisváltás

Bázisváltás, also known as base conversion, is the process of converting a number from one numerical base to another. This is a fundamental concept in mathematics and computer science, often used in various applications such as digital electronics, programming, and data representation.

The most common bases used in everyday life are decimal (base 10), binary (base 2), octal (base 8), and hexadecimal (base 16). Each base has its own set of symbols, typically the digits 0-9 and, for bases greater than 10, letters A-F.

The process of bázisváltás involves two main steps: conversion to decimal and conversion from decimal. To convert a number from any base to decimal, each digit is multiplied by the base raised to the power of its position, starting from 0 at the rightmost digit. The results are then summed to get the decimal equivalent. For example, to convert the binary number 1011 to decimal, calculate (1*2^3) + (0*2^2) + (1*2^1) + (1*2^0) = 8 + 0 + 2 + 1 = 11.

To convert a decimal number to another base, repeated division by the target base is used. The remainders from each division, read in reverse order, give the digits of the new base number. For instance, to convert the decimal number 11 to binary, divide 11 by 2 repeatedly, recording the remainders: 11/2 = 5 remainder 1, 5/2 = 2 remainder 1, 2/2 = 1 remainder 0, 1/2 = 0 remainder 1. Reading the remainders in reverse order gives the binary number 1011.

Bázisváltás is a crucial skill in understanding how computers represent and process data. It is also a key concept in various fields, including cryptography, error detection and correction, and data compression.