- Base 2 result
- 1101
- Decimal
- 13
How it works
A sign is different from bit encoding
In this signed-integer calculator, 11111111 represents decimal 255. It does not automatically mean −1 as it can in eight-bit two’s-complement encoding. Enter an explicit minus sign when you mean a negative value.
Distinguishing binary values from decimal values
Binary notation uses a different place-value base from ordinary decimal notation. The same written sequence of digits can therefore represent a different amount depending on the chosen base. Select conversion mode when changing notation and arithmetic mode when operating on binary inputs. Keep leading zeros only when a fixed bit width is relevant to your separate application.
Arithmetic: formula and assumptions
Convert positional digits to integers, perform the operation, and convert back to the chosen base.
Division returns the integer quotient and remainder. Inputs use no prefixes.
Convert decimal and binary: formula and assumptions
Interpret positional digits, then format the exact integer in the other base.
Signed integers are supported. No floating-point conversion is used.
Worked example
Using the Arithmetic example:
- First number
- 1010
- Operation
- Add
- Second number
- 11
Convert positional digits to integers, perform the operation, and convert back to the chosen base.
Example result
Base 2 result: 1101
Decimal: 13
These are illustrative inputs. Change the values to explore a different scenario.
Formula references
References explain the underlying methods; they do not imply endorsement or individual professional review of Finflo.
Common questions
Should I include a 0b prefix with a binary input?
No. Enter the binary digits directly. The selected mode already establishes the base.
Does binary division return a repeating fractional expansion?
No. The arithmetic mode returns an integer quotient and remainder rather than a fractional binary expansion.
Prepared by Finflo. See our methodology and editorial policy.