sumivo

Sumivo · Mathematics

Binary Calculator

Add, subtract, multiply and divide two binary numbers, with every result shown in both binary and decimal. Exact arithmetic on whole binary numbers.

01 / inputs

binary
binary

02 / result

A + B (BINARY)

10000

A (decimal)
10
B (decimal)
6
Sum (A + B)
10000₂ = 16
Difference (A − B)
100₂ = 4
Product (A × B)
111100₂ = 60
Quotient (A ÷ B)
1₂ r 100₂ = 1 r 4

Calculation trace

  1. 1010₂ = 10₁₀
    0
    Operand A to decimal
  2. 110₂ = 6₁₀
    0
    Operand B to decimal
  3. 10 + 6 = 16 = 10000₂
    0
    Add
  4. 10 − 6 = 4 = 100₂
    0
    Subtract
  5. 10 × 6 = 60 = 111100₂
    0
    Multiply
  6. 10 ÷ 6 = 1 remainder 4 = 1₂ r 100₂
    0
    Divide (integer)
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How it works

Each binary digit is a power of two, so 1010 in base 2 is 1×8 + 0×4 + 1×2 + 0×1 = 10 in base 10. The tool reads both operands that way, does the arithmetic on the whole numbers, and converts the answer back to binary. Addition, subtraction, and multiplication follow the ordinary rules on the decimal values; division is integer division, giving a whole-number quotient and a separate remainder (for example 1010 ÷ 110 is 10 ÷ 6 = 1 remainder 4). All of this runs on exact big integers, so results stay precise no matter how large the numbers get, unlike ordinary floating-point which loses precision past 2^53.

Assumptions & limits

  • Operands must contain only the digits 0 and 1 (an optional 0b prefix and leading zeros are allowed); anything else is rejected.
  • Division is integer division: it returns a quotient and a remainder, not a binary fraction.
  • A − B can be negative; it is shown with a minus sign rather than a two’s-complement pattern, because two’s complement needs a fixed bit width that a plain calculator does not assume.
  • Inputs are capped at 64 bits each to keep the page responsive.
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FAQ

How do I add two binary numbers?
Enter both numbers in binary and read the Sum row. For example 1010 + 110 = 10000, which is 10 + 6 = 16 in decimal. The tool shows every result in both binary and decimal.
How does binary division work here?
It is integer division. 1010 ÷ 110 is 10 ÷ 6 = 1 with remainder 4, shown as quotient 1 and remainder 100 in binary. It does not produce a binary fraction.
Why is a negative result shown with a minus sign?
When A is smaller than B, A − B is negative. Representing negatives in binary (two’s complement) requires choosing a fixed bit width, so this calculator shows the plain magnitude with a minus sign instead of assuming a width.
Is the result exact for very large binary numbers?
Yes. The arithmetic uses arbitrary-precision integers, so a 53-bit or 64-bit operand is computed exactly — no rounding of the kind ordinary floating-point introduces beyond 2^53.
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