What is a universal gate? Show how NOT, AND and OR gates can be made using only NAND gates, with truth tables.
How to lay out the answer. Follow the frame, then write it in your own words.
1 · Define it. A universal gate is one from which AND, OR and NOT, and so any logic circuit, can be built. NAND and NOR are universal.
2 · Give the NAND truth table. Y = NOT(A·B): 00 gives 1, 01 gives 1, 10 gives 1, 11 gives 0.
3 · NOT from NAND. Join both inputs: Y = NOT(A·A) = Ā.
4 · AND from NAND. A NAND followed by a NAND used as NOT gives A·B.
5 · OR from NAND. Invert A and B with two NANDs, then feed a third: Y = NOT(A′·B′) = A + B. Check it row by row.
6 · Draw the circuits. [Diagrams: NAND with joined inputs as NOT; two NANDs in series as AND; two NAND inverters feeding a third NAND as OR; A, B and Y labelled on each]
7 · Real life. Phone memory chips are built from NAND-type circuits.
8 · Close in one line. So, NAND gates alone can make every basic gate, which is why it is called universal.
Scoring tip: Write a truth table for each combination you draw. The table is the proof examiners want.
