Binary Calculator · Practical guide
How to Add Binary Numbers Step by Step
Four addition rules, a carried 1 when you hit two — binary addition is simpler than decimal.
At a glance
The Four Rules
Binary addition uses only four facts: 0 + 0 = 0, 0 + 1 = 1, 1 + 0 = 1, and 1 + 1 = 10 (write 0, carry 1). If a carry meets two 1s, then 1 + 1 + 1 = 11 — write 1, carry 1. That is the entire method.
Interactive tool
Binary Calculator
Enter your own values, then compare the result with the examples below.
Result
Worked Example: 1011 + 0110
Align the numbers on the right and work column by column from right to left:
- Column 1 (rightmost): 1 + 0 = 1
- Column 2: 1 + 1 = 10, write 0, carry 1
- Column 3: 0 + 1 + carry 1 = 10, write 0, carry 1
- Column 4: 1 + 0 + carry 1 = 10, write 0, carry 1
- Final carry becomes the new leftmost digit: 1
Reading the results left to right: 1011 + 0110 = 10001.
Check It in Decimal
1011 is 11 in decimal and 0110 is 6, and 11 + 6 = 17. Converting 10001 back: 16 + 0 + 0 + 0 + 1 = 17, so the binary answer is correct. The calculator above shows both conversions plus hexadecimal (0x11) automatically, so you can verify each hand-worked step.
Common Mistake
Most errors come from forgetting a carry after 1 + 1. When two carries chain — as in 111 + 001 = 1000 — every column produces a new carry until the sum runs out of 1s.
Frequently Asked Questions
What happens when the sum needs an extra digit?
A carry out of the leftmost column becomes a new leading 1. For example, 1111 + 0001 = 10000, which is 15 + 1 = 16 in decimal.
Do the binary numbers need to be the same length?
No. Pad the shorter one with leading zeros so the columns line up: 101 + 11 is easier as 101 + 011 = 1000.
How do I convert the binary result to decimal?
Multiply each digit by its place value (1, 2, 4, 8, 16, ...) and add. 10001 = 16 + 1 = 17. The calculator shows the decimal result alongside the binary.
Why do computers add in binary?
Digital circuits have two stable states, on and off, which map naturally to 1 and 0. Binary addition rules translate directly into simple logic gates.