Final answer:
A counter with T flip-flops for the binary sequence 0, 2, 2, 2 requires unconventional design, as the sequence has only three unique states, unlike typical binary counters. The LSB T flip-flop should have an always zero T input, while the MSB T flip-flop T input is connected to the output of the LSB flip-flop. Additional logic would be needed to lock the counter at the value 2.
Step-by-step explanation:
To design a counter with T flip-flops that goes through the binary sequence 0, 2, 2, 2, we need to consider how T flip-flops work. A T flip-flop changes state, or 'toggles', its output on every clock cycle if the T input (toggle input) is asserted (1). If the T input is not asserted (0), the output does not change. For the given sequence, the output must be 0, 2 (in binary 10), 2, 2. This implies the counter must hold the value 2 after the first count.
To achieve this, the least significant bit (LSB) T flip-flop must have a T input that is always 0 since the LSB does not change (stable at 0). The most significant bit (MSB) T flip-flop must toggle to 1 on the first count and then remain at 1; hence its T input should be connected to the output of the LSB flip-flop. However, the sequence has only three unique states, which is unconventional as counters typically operate in powers of two (binary counting).
This example can be thought of as a special case counter that is not truly binary sequential, but rather a single-transition counter from 0 to 2, then locking to 2. Due to the nature of the sequence, the standard binary up-counter design is not directly applicable, and no actual T flip-flop circuit can perpetually repeat the sequence 0, 2, 2, 2 without additional logic for resetting or controlling the flip-flops.