A 4-bit binary counter has a clock input pin CK, an active-high reset pin R, and output pins $Q_0$, $Q_1$, $Q_2$, and $Q_3$, where $Q_0$ is the least significant bit. State the type of 2-input logic gate and the counter outputs to which its inputs must be connected so that the circuit functions as a modulo-6 counter.

Table 1 shows how the values of the controller inputs $Q_2{Q}_1{Q}_0$ control the logic level applied to each of the segments $p$ to $v$ during the counting cycle of a modulo-6 counter.

Table 1

One of the logic outputs $p$ to $v$ is controlled by a single NOT gate connected to one of the inputs $Q_0$, $Q_1$, or $Q_2$. State the input that is used and the segment that this NOT gate controls.

$X$ represents one of the logic outputs. The Boolean expression for this output is:

Identify which of the logic outputs $p$ to $v$ is controlled by this function.

$Y$ represents another of the logic outputs. The Boolean expression for this output is:

Explain the configuration of logic gates (NOT, AND, NAND, OR) needed to construct a circuit representing this expression, tracing the signal path from inputs $Q_0$, $Q_1$, and $Q_2$ to output $Y$.