How this tool works

Choose Detailed to see every law applied on its own line, or Compact to merge related steps (for example, all distributions or all cleanup steps) into a single line. Both styles reach the same final answer.

The expression is parsed with standard precedence (NOT, then AND, then XOR, then OR). It is then rewritten one law at a time, and every rewrite is printed as its own line: XOR/XNOR definitions, double negation, De Morgan, null/identity, complement, idempotent, distributive, absorption, redundancy (X + X'Y = X + Y), combining (XY + XY' = X, shown as factor, complement, identity) and the consensus theorem.

The tool works purely with Boolean algebra: when no simplifying law applies, it may add a consensus term (XY + X'Z = XY + X'Z + YZ) that lets other terms combine or be absorbed, then continues until nothing more can be done.