Binary Calculator – Add, Subtract, Multiply Base 2

Binary arithmetic follows the same column rules as decimal, except carrying happens at 2 instead of 10. Adding 1011 (eleven) and 110 (six): right column 1+0 = 1; next 1+1 = 10, write 0 carry 1; then 0+1+1 = 10, write 0 carry 1; then 1+1 = 10, producing 10001 — seventeen, verified in decimal. Subtraction borrows similarly, or converts to two’s complement: to compute 1011 − 110, negate 110 in four bits (invert 0110 → 1001, add 1 → 1010), then 1011 + 1010 = 10101, and dropping the leading carry leaves 101 — five. Multiplication is shifted addition: 101 × 11 = 101 + 1010 = 1111, exactly 5 × 3 = 15. The calculator prints every carry and borrow row, the decimal cross-check, and the two’s-complement trace for negative results.

1. 1

   Enter two binary numbers

   Only 0s and 1s — the parser rejects other digits

2. 2

   Choose the operation

   Add, subtract, multiply or divide

3. 3

   Follow the carries

   Each column’s sum, carry and borrow is displayed

4. 4

   Cross-check in decimal

   The decimal equivalents confirm the binary result

• 1

  In binary, 1+1 = 10 — carry the one, write the zero

• 2

  Negative numbers use two’s complement: invert bits and add 1

• 3

  Multiplying by 2 just appends a 0: 101 → 1010

• Writing 1+1 = 2 in a column — binary has no digit 2

• Forgetting the final carry, reading 10001 as 0001

• Treating two’s complement as simple inversion without the +1

• Multiplying 101×11 as 1111×... mixing up operand order in long multiplication