Binary to Decimal Converter
Convert binary to decimal, hexadecimal, and octal โ or enter any base and convert to the others. Includes step-by-step working.
How to Convert Binary to Decimal
Each binary digit (bit) represents a power of 2, starting from 2โฐ = 1 on the right. To convert binary to decimal, multiply each bit by its corresponding power of 2 and sum the results. Example: 1101โ = (1ร2ยณ) + (1ร2ยฒ) + (0ร2ยน) + (1ร2โฐ) = 8 + 4 + 0 + 1 = 13โโ.
How to Convert Decimal to Binary
Divide the decimal number repeatedly by 2 and record the remainder at each step. Read the remainders from bottom to top. Example: 13 รท 2 = 6 remainder 1 โ 6 รท 2 = 3 remainder 0 โ 3 รท 2 = 1 remainder 1 โ 1 รท 2 = 0 remainder 1. Reading remainders bottom-up: 1101.
Binary, Decimal, Hexadecimal, and Octal
These are all number bases (positional notation systems). Binary (base-2) uses digits 0-1. Octal (base-8) uses 0-7. Decimal (base-10) uses 0-9. Hexadecimal (base-16) uses 0-9 and A-F (A=10, B=11, C=12, D=13, E=14, F=15). Computers internally use binary; hex is a compact human-readable representation of binary (each hex digit = 4 bits); octal is common in Unix file permissions.