2021 A/L Physics Past Paper · Question 10 (English Medium)

Answer: (1) NOT gate.

What the question asks

What we know:

The gate in the figure is a NAND gate. Its two inputs are joined together, and both come from one point, $X$. The output is $Y$.

What each letter means:

$X$: the one input of the circuit.

$A$ and $B$: the two inputs of the NAND gate. Here $A = X$ and $B = X$.

$Y$: the output of the circuit.

$1$ and $0$: logic 1 (high, on) and logic 0 (low, off).

We want: which single gate does the same job as this circuit.

The plan: try both values of $X$, $0$ and $1$. Find $Y$ each time. Then see which gate gives the same table.

Relevant theory

The logic operation of the NAND gate is the inverse of that of the AND gate.

A NOT can be made by connecting the two input terminals of a NAND gate together and taking it as one input.

Reading the options

Think of a door that opens only when two people push at the same time. A NAND gate is the opposite: its output goes to $0$ only when both inputs are $1$. For every other case the output is $1$.

$A = 0$, $B = 0$: output $= 1$

$A = 0$, $B = 1$: output $= 1$

$A = 1$, $B = 0$: output $= 1$

$A = 1$, $B = 1$: output $= 0$

Here both inputs come from the same wire. So $A$ and $B$ are always equal. Only two rows of the table can happen: $0, 0$ and $1, 1$.

$X = 0$

$Y = 1$

Both inputs are $0$. A NAND gate with $0$ and $0$ gives $1$.

$X = 1$

$Y = 0$

Both inputs are $1$. A NAND gate with $1$ and $1$ gives $0$.

Each output is the opposite of the input: a NOT gate.

Both inputs are $0$. NAND gives $1$.

Both inputs are $1$. NAND gives $0$.

Look at the two rows above.

The output is always the opposite of the input. That is exactly what a NOT gate does.

$$Y = \overline{X}$$

This says: $Y$ is "not $X$". So the answer is option (1).

Why the other options fail

An OR gate would give $1$ when $X = 1$. Here $Y = 0$.

The small circle at the output turns the AND answer upside down. $X = 1$ gives $Y = 0$.

The gate drawn is a NAND gate, and the circuit has only one input.

The two inputs are always the same, yet $Y = 1$ when $X = 0$. That is not EXOR.

Conclusion

Does it make sense?

A NAND gate is an AND gate followed by a NOT. Joining the inputs makes the AND part pass $X$ straight through, because $X$ AND $X$ is just $X$. Only the NOT part is left.

So the circuit is a NOT gate.

$Y = \overline{X}$

Both inputs of the NAND gate are $X$. $X = 0$ gives $Y = 1$, and $X = 1$ gives $Y = 0$.

The output is always the opposite of the input, $Y = \overline{X}$. It is a NOT gate. The answer is (1).

When the inputs of a gate are joined, only the rows with equal inputs can happen. Write just those rows.

A NAND or a NOR gate with joined inputs is a NOT gate.

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