Convert numbers instantly between binary, octal, decimal, and hexadecimal with a live place-value breakdown showing exactly how each digit contributes to the total.
A base converter translates a number from one positional numeral system into another — most commonly between binary (base 2), octal (base 8), decimal (base 10), and hexadecimal (base 16). Every number system works the same way: each digit's value depends on its position, multiplied by the base raised to that position's power. Computers store and process everything in binary, but binary strings get long and hard to read, so programmers use hexadecimal as a compact shorthand, and octal shows up in older Unix file permissions.
This calculator instantly converts your input across all four bases at once, and shows the place-value breakdown — each digit times its positional weight — so you can see exactly how the conversion works rather than just getting an opaque answer.
Converting hexadecimal 2F to decimal: 2×16¹ + 15×16⁰ = 32 + 15 = 47. In binary, 47 is 101111, and in octal it's 57.