Binary linear equation solver

Binary linear equation solver calculator can be used for solving equations of the form ax + by = c where a, b, and c are binary numbers.

Input Parameters

Calculation Results

Calculation Formula

The solution (x, y) is calculated such that ax + by = c.

Where:
a, b, c are binary coefficients.
x, y are binary variables.

Solution

Enter the coefficients and click Calculate to see the solution.

Binary linear equation solver Calculator Usage Guide

Learn how to use the Binary linear equation solver calculator and its working principles

How to use the calculator

  1. Enter the coefficients a, b, and constant c as binary numbers (0 or 1). For example, enter 1 for binary one, and 0 for binary zero.
  2. Click the "Calculate" button to solve the equation.
  3. The calculator will display the particular solution (x₀, y₀) and the general solution in both binary and decimal forms.

Working principle

This calculator solves equations of the form ax + by = c where:

  • a, b, and c are binary coefficients (0 or 1)
  • x and y are binary variables (0 or 1)

The solution is found using the Extended Euclidean Algorithm to find a particular solution, and then the general solution is derived from it.

Example

Consider the equation 1x + 1y = 1 (binary):

Enter a = 1, b = 1, c = 1 in the calculator and click Calculate.

The solution will be x = 1, y = 0 (binary) or x = 1, y = 0 (decimal).

Notes

The calculator assumes that a, b, and c are integers represented in binary form. If the equation has no solution (i.e., c is not divisible by gcd(a, b)), the calculator will indicate that no solution exists.