$3.$ You are to design a tree$-$structured combinational circuit that detects the presence in a binary input vector $\backslash ($ V $\backslash )$ of length $\backslash ($ N $\backslash )$ of an alternating pattern consisting of zero, one or two $0$ s ; followed by two $1$ s ; followed by two $0$ s ; etc.; ending with zero, one or two $1$ s $.$ To have the required pattern, the centre portion of a vector $\backslash ($ V $\backslash )$ must contain the alternating $00110011$ pattern, but the pattern may be truncated at the ends. The length $\backslash ($ N $\backslash )$ of input vector $\backslash ($ V $\backslash )$ is constrained to be a multiple of $3.$ To match this constraint, the leaf nodes of the circuit are to receive as inputs three adjacent bits of $\backslash ($ V $\backslash ).$ Each internal node in the circuit is to combine outputs produced by either two adjacent leaf nodes, or two internal nodes at the next higher level in the tree. The root node is to produce an output of $1$ if the pattern was detected in $\backslash ($ V $\backslash )$; otherwise, the output is to be $0$ to indicate that the pattern was not found in $\backslash ($ V $\backslash ).$ Your solution should provide a diagram that illustrates the arrangement of the cells for a tree network that handles binary vectors of length $24.$ Hint: It may be useful for the leaf nodes and the internal nodes to produce, among their output signals, one signal that is $1$ if the input vector bits lying above the node are consistent with the desired alternating pattern being detected so far; otherwise, that one particular signal will be $0$ to indicate that the alternating pattern cannot be present. $[35$ marks$]$