Boolean algebra basics
Digital electronics basics · Physics
DC circuit
Interactive 3DElectrons drift around the loop — raise the voltage and watch the current obey Ohm's law.
Controls
Drag the sliders or type a value — the simulation updates live.
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1V12V
Study notes
Worked example: Simplify Y = Ā·B̄ + A·B̄ + Ā·B using Boolean algebra. Step 1: Group the first two terms — they share B̄: Ā·B̄ + A·B̄ = B̄·(Ā + A). Step 2: Ā + A = 1 (complement law), so the group becomes B̄·1 = B̄. Step 3: Now Y = B̄ + Ā·B. Use the absorption-style rule X + X̄·Z = X + Z with X = B̄, Z = Ā: B̄ + B·Ā... careful: X̄ = B, so B̄ + B·Ā = B̄ + Ā. Step 4: Final simplified form: Y = Ā + B̄. By De Morgan, this also equals ¬(A·B) — a single NAND gate! Check with truth table (A=1,B=1): original = 0+0+0 = 0; simplified = 0+0 = 0. Matches.