How this calculator works
Add from the rightmost bit. A column total of two writes 0 and carries 1; a total of three writes 1 and carries 1. The exact result can need one more bit than the inputs. Missing-addend modes subtract the known addend from the exact sum. Select unsigned or two's complement interpretation before entering patterns. Short inputs are padded with zeros to the selected width; signed negatives therefore need a leading 1 at that width. Overflow describes the exact mathematical answer, which is never silently discarded.
Formula
Sum = A + B. For a column: bit = (a + b + carry) mod 2; next carry = floor((a + b + carry)/2).
Worked example
1011 + 0110 = 10001, because 11 + 6 = 17. In four bits the stored result is 0001 and unsigned overflow is reported.
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Frequently asked questions
What does the selected width change?
It limits each operand and determines the stored result and signed interpretation. The exact answer is also displayed, even when it needs more bits.
How are negative inputs entered?
Choose two's complement and enter the complete negative pattern for the chosen width. For example, 11111111 is -1 in eight bits. A minus sign is only accepted in the exact sum field for missing-addend calculations.
Are long binary strings exact?
Yes. Operands are text strings and calculations use integer arithmetic with no rounding. Presets reach 64 bits and custom widths reach 256 bits.
What do the steps show?
Column carries are listed from the least significant bit upwards. A carry leaving the final column belongs to the exact result.