Results

Result (Binary)

Result (Decimal, wrapped to width)

True Sum (Decimal, unbounded)

Overflow

Addend A (Padded Binary)

Addend B (Padded Binary)

Binary Addition Calculator

Our Binary Addition Calculator adds two binary numbers together and shows the result in both binary and decimal — including a warning when the true sum is too large to fit in your chosen bit width.

How Binary Addition Works

Binary addition follows the same column-by-column method as decimal addition, using just four rules: 0+0=0, 0+1=1, 1+0=1, and 1+1=10 (write 0, carry 1 to the next column). When the final carry has nowhere left to go — because every bit position in the chosen width is already used — the result has overflowed: the true sum no longer fits, and the binary result you see has wrapped around.

Example Calculations (8-bit)

A: 1100 (12), B: 1010 (10)

00001100 + 00001010 = 00010110

✓ Result = 22, no overflow

A: 11111111 (255), B: 1 (1)

11111111 + 00000001 = 100000000 — 9 bits, but only 8 are available

✓ True Sum = 256, wrapped Result = 00000000, Overflow = Yes

Features of Our Binary Addition Calculator

✅ Detects overflow automatically

✅ Choose 4, 8, 12, 16, 32, 64-bit, or a custom bit width

✅ Shows both the wrapped and true unbounded sum

✅ Free to use, no sign-up required

Who Can Use This Calculator?

Students – For computer science and digital logic homework

Programmers – For debugging overflow bugs in low-level code

Teachers – For demonstrating carry and overflow step by step

Puzzle Solvers – For quick binary arithmetic checks

👉 Try our Binary Addition Calculator to add any two binary numbers instantly.