decimalkonvertering

Decimalkonvertering refers to the process of converting numbers from one base system to another, specifically involving the decimal (base-10) system. Most commonly, it involves converting from a non-decimal base, such as binary (base-2), octal (base-8), or hexadecimal (base-16), into the decimal system. This conversion is fundamental in computing and mathematics.

To convert a number from another base to decimal, each digit is multiplied by the base raised to the power of its position. Positions are counted from right to left, starting with zero. For example, the binary number 1101 is converted to decimal by calculating (1 * 2^3) + (1 * 2^2) + (0 * 2^1) + (1 * 2^0), which equals 8 + 4 + 0 + 1 = 13.

Similarly, an octal number like 257 is converted by (2 * 8^2) + (5 * 8^1) + (7 * 8^0), resulting in (2 * 64) + (5 * 8) + (7 * 1) = 128 + 40 + 7 = 175 in decimal. Hexadecimal conversion follows the same principle, but uses base-16 and the digits A-F represent values 10-15. For instance, hexadecimal 1A is (1 * 16^1) + (10 * 16^0) = 16 + 10 = 26 in decimal.

Decimalkonvertering is also used in the reverse process, converting decimal numbers to other bases. This is typically achieved through repeated division by the target base, with the remainders forming the digits of the converted number from right to left. This understanding is crucial for interpreting data represented in various numerical systems.