Binary Arithmetic Calculator Formula

Understand the math behind the binary arithmetic calculator. Each variable explained with a worked example.

Use the Binary Arithmetic Calculator

Formulas Used

Sum Val

sum_val = a + b

Diff Val

diff_val = a - b

And Val

and_val = bitAnd(a, b)

Or Val

or_val = bitOr(a, b)

Xor Val

xor_val = bitXor(a, b)

Variables

VariableDescriptionDefault
aNumber A42
bNumber B15

How It Works

Binary Arithmetic

Bitwise Operations

  • AND: both bits must be 1 → result is 1
  • OR: at least one bit must be 1 → result is 1
  • XOR: exactly one bit must be 1 → result is 1

    • Example: 42 AND 15

  • 42 in binary: 101010
  • 15 in binary: 001111
  • AND result: 001010 = 10

    • Bitwise operations work on individual bits of the binary representation.

    Worked Example

    Binary operations on 42 and 15.

    a = 42b = 15
    1. 0142 + 15 = 57
    2. 0242 - 15 = 27
    3. 0342 AND 15: 101010 AND 001111 = 001010 = 10
    4. 0442 OR 15: 101010 OR 001111 = 101111 = 47
    5. 0542 XOR 15: 101010 XOR 001111 = 100101 = 37

    Ready to run the numbers?

    Open Binary Arithmetic Calculator