A calculator for converting between binary and decimal numbers and performing binary arithmetic operations. Useful for programming, computer science learning, and digital logic circuit design.
Binary is a number system that uses only two digits: 0 and 1. Computers process all data in binary, representing the ON/OFF states of digital circuits. For example, decimal 5 is 101 in binary, and decimal 10 is 1010 in binary.
To convert binary to decimal, multiply each digit by powers of 2 and sum them. For example, binary 1011 is (1×2³)+(0×2²)+(1×2¹)+(1×2⁰) = 8+0+2+1 = 11 (decimal). This calculator performs these conversions instantly.
To convert decimal to binary, repeatedly divide the decimal number by 2 and read the remainders in reverse order. For example, converting decimal 13: 13÷2=6 remainder 1, 6÷2=3 remainder 0, 3÷2=1 remainder 1, 1÷2=0 remainder 1, reading in reverse gives 1101 (binary).
Binary addition follows the rules: 0+0=0, 0+1=1, 1+0=1, 1+1=10 (carry occurs). For example, 101 + 11 = 1000. Subtraction borrows 2 from higher places when needed. This calculator automatically handles carries and borrows.
Binary multiplication is similar to decimal but simpler. The only rules are: 0×0=0, 0×1=0, 1×0=0, 1×1=1. Division works the same as decimal division but calculated in binary. In programming, bit shift operations enable fast multiplication/division.
Binary is widely used in computer programming, network subnet mask calculations, file permission settings (chmod), digital image processing, encryption, and more. Many computer-related tasks like IP addresses, MAC addresses, bit flags, and color codes are based on binary.