Binary Calculator

This specialized calculator performs arithmetic operations (addition, subtraction, multiplication, division) on numbers represented in binary notation (base-2 numbering system using only 0 and 1 digits). The tool accepts binary input strings, validates digit correctness, executes computations through bit manipulation or conversion algorithms, and displays results in binary format with optional decimal equivalents for verification.

Binary addition implements logic mirroring elementary addition but with base-2 carry rules: 0+0=0, 0+1=1, 1+0=1, 1+1=10 (zero with carry). The algorithm processes bits right-to-left using full adder logic with carry propagation through each position. Subtraction employs two's complement representation for negative numbers, converting subtraction operations into addition of negative values. Multiplication occurs through shift-and-add algorithms or repeated addition, while division uses long division adapted for binary arithmetic or successive subtraction approaches.

Advanced features include bitwise logical operations (AND, OR, XOR, NOT), bit shifting for quick multiplication/division by powers of two, and signed number support using two's complement notation. The calculator displays step-by-step solutions showing carry propagation, borrow operations, or intermediate shift states for educational purposes. Users learn computer arithmetic fundamentals, verify assembly language calculations, debug low-level code, or solve computer science coursework problems. The interface typically provides result conversion to hexadecimal and decimal simultaneously, facilitating quick verification of binary computation accuracy.