How binary arithmetic works
Binary (base 2) uses only the digits 0 and 1. Each position is a power of two — from the right, 1, 2, 4, 8, 16, and so on:
10112 = 1·8 + 0·4 + 1·2 + 1·1 = 1110
To compute reliably, this tool converts each binary string to a decimal integer, performs the operation, then converts the result back to binary. The same carry-and-borrow rules you use in base 10 apply in base 2 — you just carry at 2 instead of 10.
Worked example
1011 + 110:
Decimal values: 1011₂ = 11, 110₂ = 6.
Add: 11 + 6 = 17.
Back to binary: 17 = 10001₂ (hex 0x11).
Binary, decimal and hexadecimal
Computers store everything in binary, but long binary strings are hard to read, so programmers often use hexadecimal (base 16), where each hex digit packs exactly four bits. This calculator shows all three bases so you can move between how a machine stores a value and how humans read it.
Tip: to convert a single number between bases without arithmetic, use the hex to decimal converter.