Binary Calculator

Convert between decimal, binary, octal, and hexadecimal number systems and perform binary operations online.

Input Value

Input Base

Target Base

About Binary Numbers and Operations

Binary (Base 2): Uses only 0 and 1. Each position represents a power of 2 (1, 2, 4, 8, 16, etc.). E.g., binary 1011 = (1×8) + (0×4) + (1×2) + (1×1) = 11 in decimal.
Decimal (Base 10): Our standard number system using digits 0-9.
Hexadecimal (Base 16): Uses digits 0-9 and letters A-F (representing values 10-15). E.g., hex A3 = (10×16) + (3×1) = 163 in decimal.
Octal (Base 8): Uses digits 0-7. Each position represents a power of 8. E.g., octal 27 = (2×8) + (7×1) = 23 in decimal.

Arithmetic Operations: Addition, subtraction, multiplication, and division follow similar rules as decimal, but with only two digits (0 and 1).
Bitwise AND: For each bit position, returns 1 only if both input bits are 1. (E.g., 1010 AND 1100 = 1000)
Bitwise OR: For each bit position, returns 1 if at least one input bit is 1. (E.g., 1010 OR 1100 = 1110)
Bitwise XOR: For each bit position, returns 1 if exactly one input bit is 1. (E.g., 1010 XOR 1100 = 0110)
Bitwise NOT: Inverts each bit, changing 0 to 1 and 1 to 0. (E.g., NOT 1010 = 0101)
Shift Operations: Move bits left or right, essentially multiplying or dividing by powers of 2.

Binary is fundamental in computing since digital electronics use binary signals (on/off, high/low). Applications include: