Physics · Semiconductor Electronics : Materials, Devices And Simple Circuits · NEET
A gate is universal if you can build the three basic gates (NOT, AND, OR) using only copies of that one gate. Since NOT, AND and OR together can make ANY logic circuit, being able to build all three means you can build anything. NAND alone can do this, and NOR alone can do this. That is why both are called universal gates. AND, OR and NOT are NOT universal on their own because, for example, you cannot make a NOT gate from AND gates only.
Join both inputs of the NAND gate together and feed the same signal A into both. NAND output = (A . A)' = A'. When A = 0 you get 1, when A = 1 you get 0. That is exactly a NOT gate. The same trick works for NOR: tie both inputs together, output = (A + A)' = A'.
AND = NOT of NAND. First NAND gives (A . B)'. Then pass that through a second NAND used as a NOT (both inputs tied). Final output = ((A.B)')' = A.B. So two NAND gates make one AND gate.
Use De Morgan's law: A + B = (A' . B')'. Invert A with one NAND-as-NOT, invert B with another NAND-as-NOT, then feed A' and B' into a third NAND. Output = (A' . B')' = A + B. So three NAND gates make one OR gate.
AND gives output 1 only when BOTH inputs are 1. NAND is the exact opposite of AND: it gives 0 only when both inputs are 1, and 1 in every other case. In symbols, NAND = (A . B)'. The little bubble on the gate symbol means "NOT", so NAND is literally AND with a NOT stuck on the output.
Write the Boolean expression at the output, then simplify using De Morgan's laws: (A . B)' = A' + B' and (A + B)' = A' . B'. A very common NEET trap is: invert both inputs, then feed into a NOR. Output = (A' + B')' = A . B, which is an AND gate. If inputs are inverted then fed to a NAND, output = (A' . B')' = A + B, an OR gate. Learn these two patterns and most questions become one step.
In a circuit each input (A and B) is first passed through a NOT gate, and the two inverted signals are fed into a NOR gate to give output Y. The given circuit is equivalent to a single:
Each input is inverted and then both inverted inputs are fed to a NOR gate to produce output Y. The output Y is similar to the output of a/an:
Two NOR gates each receive the same inputs A and B, and their outputs are fed into a final AND gate to give Y. The output Y is similar to the output of a/an ____ gate.
Try the real previous-year questions from this chapter — each with the answer and a full solution.
Both NAND and NOR are universal gates. Each one alone can build NOT, AND and OR, and therefore any logic circuit. So the correct answer to "which is universal" is: both of them.
Because no single one of them can build all three basic operations. For example, you cannot create a NOT (inversion) using only AND gates or only OR gates. You always need an inverter that they cannot supply, so they are not universal by themselves.
Three NAND gates. Two are used as NOT gates to invert A and B, and the third NANDs the inverted inputs: (A' . B')' = A + B, which is OR.
Two NAND gates. The first gives (A . B)', and the second (used as a NOT with both inputs tied) inverts it back to A . B.
NAND: for inputs (00, 01, 10, 11) the output is 1, 1, 1, 0 (it is 0 only when both inputs are 1). NOR: for inputs (00, 01, 10, 11) the output is 1, 0, 0, 0 (it is 1 only when both inputs are 0).
No. XOR (exclusive OR) is not universal because you cannot build every gate from XOR alone; in particular you cannot make an AND or a constant using only XOR gates. Only NAND and NOR are universal.
