A full lesson: a cartoon movie to start, then digital signals and the OR, AND and NOT gates, NAND and NOR, Boolean rules and timing diagrams, NAND and NOR as universal gates, gate combinations to crack, NEET shortcuts, problems to solve yourself, and 12 MCQs.
Every decision in the shop is a yes-or-no rule: 1 or 0. An OR gate says "any one is enough", an AND gate says "all of them, please", and a NOT gate says "the opposite". With NAND gates alone you can build all three.
Ramesh uncle runs the kirana shop at the corner, and Arjun is helping him wire it up. Uncle has three rules. Rule 1: at night, the bell must ring if the front shutter or the back window is opened. Rule 2: the cash locker opens only with uncle's key and aunty's key. Rule 3: the sign-board lamp is on when it is not daytime.
Each rule takes yes/no inputs and gives a yes/no output. In electronics "yes" is a high voltage, written 1, and "no" is a low voltage, written 0. A signal that has only these two levels is a digital signal (an analog signal, like a sine wave, can take any value). A circuit that applies such a rule is a logic gate, and the list of outputs for every input combination is its truth table.
"OR, AND, NOT are just the words you already use every day. 'Tea or coffee, either is fine.' 'Bring your admit card and your ID.' 'Do not enter.' We only write them with 1s and 0s."
"For Rule 1, list all the ways the two doors can be (open or shut). In how many of them does the bell ring?"
Four combinations: both shut, only shutter open, only window open, both open. The bell rings in three of them: every case except "both shut".
Pick a gate. Tap the switches A and B on the picture (or a row of the truth table) and watch the output lamp Y. Orange wires carry 1, grey wires carry 0. Press "Auto" to step through every row.
1 when at least one input is 1. In Boolean algebra 1 + 1 = 1: the plus sign means OR, not ordinary addition.
1 only when both inputs are 1. Like two switches in series.
One input, inverted: 0 → 1, 1 → 0. Also called an inverter.
"OR is a lenient teacher: one correct answer is enough. AND is a strict teacher: everything must be correct. NOT is the naughty student: always says the opposite."
A NAND gate is an AND gate followed by a NOT gate; a NOR gate is an OR gate followed by a NOT gate. The small circle (bubble) at the output of a symbol means NOT. Switch on "Show inside" to see the two-gate version and the extra column in the table.
| A B | OR | AND | NAND | NOR |
|---|---|---|---|---|
| 0 0 | 0 | 0 | 1 | 1 |
| 0 1 | 1 | 0 | 1 | 0 |
| 1 0 | 1 | 0 | 1 | 0 |
| 1 1 | 1 | 1 | 0 | 0 |
"To write a NAND table, write the AND column and flip every value. NAND is 0 only when both inputs are 1. NOR is 1 only when both inputs are 0."
"Which gate gives 1 for exactly one input combination, and which gives 0 for exactly one combination?"
AND and NOR are 1 for exactly one row (1 1 and 0 0). OR and NAND are 0 for exactly one row (0 0 and 1 1).
NEET often gives the inputs as waveforms and asks for the output waveform. Tap any slot of A or B to flip it, choose a gate, and the output Y is worked out slot by slot. The yellow column moves along time.
One 1 is enough to make the OR output 1.
One 0 is enough to make the AND output 0.
Two inverters in a row cancel.
"Break the bar, change the sign." These two lines explain every universal-gate trick in Stage 5.
"For a waveform question, never look at the whole picture at once. Cut time into slots wherever any input changes, write A and B for each slot, and apply the truth table slot by slot."
Using only NAND gates you can build NOT, AND and OR, and so any digital circuit. The same is true for only NOR gates. Choose a build, tap the inputs, and check that the table matches the gate it imitates. The middle column shows the hidden wire inside.
1 NAND (or 1 NOR, since (A + A)‾ = Ā).
2 NAND gates: ((A · B)‾)‾ = A · B. Likewise OR = NOR followed by NOR-as-NOT.
3 NAND gates: invert both inputs, then NAND them (De Morgan). Likewise AND = NOR of Ā and B̄, 3 NOR gates.
"A factory can make one kind of chip, millions of times, and still build any computer. That chip is NAND. Count for NEET: NOT needs 1, AND needs 2, OR needs 3 NAND gates. For NOR, swap AND and OR."
NEET loves a small network of gates and four options. Pick a circuit, tap the four input rows, fill the table in your head, and then name the single gate it behaves like. (XOR gives 1 when the inputs differ; XNOR gives 1 when they are the same. These are beyond the NEET list, but the method is the same.)
Write the intermediate outputs as columns P, Q, … and finish the table. Then match the Y column to a known gate.
Ramesh uncle's three rules. A full adder in a calculator, the checker in a microwave door and every computer are built the same way, from millions of gates.
NAND and NOR are the same with every output flipped: NAND only 11 → 0, NOR only 00 → 1.
A bubble at an output inverts the output; bubbles at both inputs invert the inputs. "Bubbled-input AND" = NOR, "bubbled-input OR" = NAND.
AND(A, A) = OR(A, A) = A: just a wire.
NOR: NOT 1 · OR 2 · AND 3.
NOT gates on both inputs of a NAND → OR; on both inputs of a NOR → AND.
Mark a vertical line wherever any input changes and apply the table in each slot.
"Never trust a circuit's looks. Two NOT gates and a NAND look complicated, but the table says OR. Fill the four rows, and the answer is sitting there."
Cover the solution, draw the truth table, and solve on paper. Open the hint only if you are stuck for more than a minute.
Write the truth table of Y = (A · B)‾ and name the gate.
Write the A · B column first, then flip it.
Both inputs of a NOR gate are joined and connected to A. Find Y for A = 0 and A = 1. What is the circuit?
Y = (A + A)‾ and A + A = A.
A and B pass through NOT gates, and the two outputs feed a NAND gate. Find the output and name the equivalent gate.
Y = (Ā · B̄)‾. Use De Morgan, or make the table.
A and B feed an AND gate and also a NOR gate. The outputs P (AND) and Q (NOR) feed an OR gate whose output is Y. Make the truth table of Y. For which inputs is Y = 1?
Columns: A, B, P = A·B, Q = (A + B)‾, Y = P + Q.
In four equal time slots, A = 0, 0, 1, 1 and B = 0, 1, 0, 1. Find the output sequence of (a) a NAND gate and (b) a NOR gate.
Go slot by slot. NAND is 0 only for 11; NOR is 1 only for 00.
Write the truth table first, then click.
Score: 0 / 12
| If the question says… | Write this first | The trap |
|---|---|---|
| "output of the combination of gates" | label wires, 4-row table | Guessing from the shape of the circuit |
| "Y = A + B" / "1 + 1 =" | Boolean OR: 1 + 1 = 1 | Writing 2 (ordinary addition) |
| "universal gates" | NAND and NOR | Choosing AND and OR, the "basic" gates |
| "inputs of a NAND / NOR joined" | NOT gate | Saying it becomes AND or OR |
| "NOT gates on both inputs of NAND" | OR (De Morgan) | Answering AND or NOR |
| "input waveforms are shown" | cut into slots, apply table | Missing a slot where only one input changes |
| "output is 0 only when both inputs are 1" | NAND | Confusing with NOR (1 only when both inputs are 0) |
| "number of NAND gates for OR / AND" | 3 / 2 | Swapping the NAND and NOR counts |
This completes the chapter. Try the Semiconductor Electronics Challenge to mix rectifiers, special diodes and logic gates in timed NEET-style sets.
Conventions: 1 = high voltage (true), 0 = low voltage (false); + = OR, · = AND, bar = NOT. XOR and XNOR are enrichment beyond the NEET list.
Follow the four steps: understand it, remember it, try it, then prove it with past papers.