Level 5: Strict choice

Open the level →Where it fits in the machine →

Task

Goal: build an Exclusive OR (XOR) gate.

XOR outputs 1 when the inputs differ and 0 when they match. It means one or the other, but not both.

The main idea: XOR works as a controlled inverter: input B decides whether A passes as is or inverted. A control input like this will be needed by the multiplexer and the ALU.

Path to this level

The competencies this level develops and their formation levels.

NAND universality · ур. 2, 3, 4 Boolean composition · ур. 3, 4

Related Materials

Solution for self-check

Try building the circuit yourself first. The solution below is a way to check yourself if you're stuck or have already solved it.

What you should get: 1 on the output when the inputs differ, 0 when they match.

Formula: XOR = (A OR B) AND NOT(A AND B). The first part answers is there at least one 1; the second answers are they not both 1.

  1. Feed A and B into OR. Its output is 1 if there is at least one 1.
  2. Feed A and B into NAND. Its output is 1 except when A=1 and B=1.
  3. Feed the OR and NAND outputs into the AND inputs.
  4. Connect the AND output to Output.

AND fires only when both conditions hold: there is a 1, but not two of them. That means the inputs differ.

Compare with OR: tea or coffee is XOR, you pick one. OR would pass tea and coffee at the same time.

Solution circuit for level 5 — Strict choice
The authored solution for level 5 in the simulator (dark theme)

Check yourself

Why can XOR not be replaced by a plain OR?

OR outputs 1 when both inputs are 1, while XOR outputs 0 in that case.