Final answer:
A sequential circuit can be designed to count the 4-bit even numbers using flip-flops and logic gates. The circuit counts through the even numbers sequentially, resetting to 0 after reaching 14.
Step-by-step explanation:
A sequential circuit can be designed to count only the 4-bit even numbers by using a combination of flip-flops and logic gates. One possible circuit design is to use four D flip-flops connected in series, with each flip-flop representing one bit of the 4-bit number. The clock signal is used to trigger the flip-flops, and the output of each flip-flop is connected to the input of the next flip-flop. By setting the initial state of the flip-flops to represent the number 0, and propagating the carry from one flip-flop to the next, the circuit will count through the even numbers sequentially.
For example, if the circuit is initially set to represent the number 0, the binary representation is 0000. When the clock signal triggers the circuit, the output will become 0001, representing the number 2. On subsequent clock signals, the output will change to 0010 (representing 4), 0011 (representing 6), and so on, until it reaches 1110 (representing 14). At this point, the circuit resets to 0000 and starts counting again.