Binary Calculator

Binary addition follows simple rules: 0+0=0, 0+1=1, 1+0=1, 1+1=10 (0 with carry 1), and 1+1+1=11 (1 with carry 1). You add column by column from right to left, carrying over just like decimal addition. Example: 1011 + 1101 = 11000₂ (11 + 13 = 24₁₀).

Binary subtraction uses borrowing: 0-0=0, 1-0=1, 1-1=0, 0-1=1 (with borrow). When subtracting 1 from 0, you borrow from the next higher bit, which gives you 10₂ (2) minus 1 = 1. Alternatively, you can add the 2's complement of the subtrahend.

Binary multiplication is simpler than decimal because you only multiply by 0 or 1. Multiply the binary number by each bit of the multiplier: if the bit is 1, copy the number (shifted left); if 0, write zeros. Then add all partial products. Example: 101 × 11 = 1111₂ (5 × 3 = 15₁₀).

Binary overflow occurs when the result of an arithmetic operation exceeds the maximum value that can be represented with the given number of bits. For unsigned 8-bit numbers, overflow happens above 255 (11111111₂). For signed 8-bit, overflow occurs above 127 or below -128. Overflow can cause unexpected results in programs.

Yes, binary division works like long division in decimal but simpler since you only compare with 0 or 1. At each step, check if the divisor fits into the current portion: if yes, write 1 and subtract; if no, write 0 and bring down the next digit. The process continues until all digits are processed.

Binary arithmetic has four basic operations: Addition (0+0=0, 0+1=1, 1+1=10), Subtraction (0-0=0, 1-0=1, 1-1=0, 10-1=1), Multiplication (0×0=0, 0×1=0, 1×1=1), and Division (0÷1=0, 1÷1=1). All follow the same principles as decimal arithmetic but with only two digits.