a) State Diagram and Sequential Circuit Type Sequential Circuit Type : This counter seems most suitable as a Moore machine because the output (which is the display of the current digit) is based solely on the state and not directly on the input. The state changes, however, will be influenced by the input x(forward or backward) State Diagram : Each state will represent a digit in your sequence "121200141". The transitions between states will depend on the value of x Here's a simplified state diagram to visualize: Here is the updated and corrected state diagram that now accurately displays each position in the sequence "121200141" as a distinct state, from S 0 S0 S 0 to S 8 S8 S 8 . The transitions for both forward counting ( x = 1 x=1 x = 1 ) and backward counting ( x = 0 x=0 x = 0 ) are properly represented, linking each state to the next or previous in the sequence. Explanation: In this diagram: States: Represented by the digits. Transitions: Arrows show the movement from one state to another based on the input x. b) Number of State Variables and Binary Codes State Variables: To uniquely identify each state, determine how many bits are needed. The sequence 121200141 has 9 unique states/digits. Thus, at least 4 bits are required to represent these states (since 2 3 = 8 2^3 = 8 which is less than 9, but 2 4 = 16 2^4 = 16 can cover up to 16 states). Binary Codes: Assign binary codes to each state sequentially. For instance: 0: 0000 1: 0001 2: 0010 3: 0011 4: 0100 (and so forth up to) 9: 1001 c) Type of Flip-Flops and State Table Type of Flip-Flops: JK flip-flops are suitable for this application because they can be easily configured to toggle, set, or reset based on the control inputs, which matches well with the counting mechanism required here. State Table: The state table will reflect the current state (based on the binary codes above), the next state when x = 1 x = 1 x = 1 (forward count), the next state when x = 0 x = 0 x = 0 (backward count), and the corresponding JK flip-flop inputs to achieve these transitions. Explanation: The state table should consider both current state and input to define the next state and outputs. The reverse characteristic of a D Flip-Flop is that the next state Q n e x t Q_{next} is simply the value at the input D D . d) Boolean Functions To obtain the Boolean functions for the D inputs: Let q 1 q_1 and q 0 q_0 be the current state bits, and D 1 D_1 and D 0 D_0 be the inputs to the D flip-flops. Boolean expressions based on the state transitions : D 1 = q 1 q 0 ‾ D_1 = q_1 \overline{q_0} (transitions to state 2 or 4 from states 1 and 0) D 0 = q 1 ‾ ( q 0 ⊕ x ) + q 1 q 0 ‾ x D_0 = \overline{q_1} (q_0 \oplus x) + q_1 \overline{q_0} x (handles the toggling between states based on input x x

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