Binary Addition Calculator — Add Binary Numbers
Enter two binary numbers to find their sum. The calculator shows the result in binary, decimal, and hexadecimal, plus a column-by-column carry trace so you can follow each step.
Binary: 10111 • Hex: 0x17
Addend A
Addend B
Carry row
Sum
- 1
A in decimal
10 - 2
B in decimal
13 - 3
Sum A + B
10 + 13 = 23
How does this calculator work?
Binary addition works column by column: 0+0=0, 1+0=1, 1+1=10₂ (write 0, carry 1). Each column sums its two bits plus any carry-in, then passes a carry-out left. Enter two binary numbers above to see the result in binary, decimal, and hex with the full carry trace.
Formula
How this is calculated
Binary addition follows the same column-by-column algorithm as decimal addition, but each column can only hold the digits 0 and 1. Each column receives three inputs: the bit from A, the bit from B, and a carry from the column to the right. There are four column cases: 0+0+0=0 (sum 0, carry 0), 0+1+0=1 (sum 1, carry 0), 1+1+0=10₂ (sum 0, carry 1), and 1+1+1=11₂ (sum 1, carry 1). The carry propagates leftward column by column — this is the ripple-carry method used inside every digital adder.
The calculator pads the shorter number with leading zeros so both operands are the same width, adds one extra bit for a possible carry into a new most-significant position, then processes columns from right (LSB) to left (MSB). The carry-row display shows which bit positions generated a carry so you can trace the computation step by step.
All arithmetic uses arbitrary-precision integers (JavaScript BigInt), so there is no overflow regardless of input length.
Frequently asked questions
Binary is base 2, so a column sum of 2 cannot be written as a single digit. It becomes 10₂: the 1 carries to the next column and the 0 stays in the current position — exactly like carrying in decimal when a column reaches 10.
The carry bit is the overflow from one column's addition that gets added to the next more-significant column. When two 1-bits add to give 2 (= 10₂), the current column records 0 and passes 1 as a carry to the column to its left.
Pad the shorter number with leading zeros on the left to match the longer number's length, then add column by column from right to left. This calculator does that automatically.
Also known as
TG we-Calculate Editorial Team. (2026). Binary Addition Calculator — Add Binary Numbers [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/binary-addition-calculator
TG we-Calculate Editorial Team. "Binary Addition Calculator — Add Binary Numbers." TG we-Calculate. 2026. https://we-calculate.com/calculator/binary-addition-calculator.
TG we-Calculate Editorial Team, "Binary Addition Calculator — Add Binary Numbers," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/binary-addition-calculator
@misc{wecalculate_binary_addition_calculator, title = {Binary Addition Calculator — Add Binary Numbers}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/binary-addition-calculator}}, year = {2026}, note = {TG we-Calculate} }
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