(Solved): The state diagram below shows a 3-bit up/down counter. When \( x=0 \), the counter counts upwards ...

The state diagram below shows a 3-bit up/down counter. When \( x=0 \), the counter counts upwards successively from 000 to 111 , then goes restarts again ("rolls over") at 000 . Similarly when \( x=1 \), the counter counts backwards from 111 to 000 , then rolls over again to 111 and continues counting down. Flipping \( x \) (e.g. 0 to 1 or 1 to 0 ) in between will change the direction of the count. We want to Implement this counter using three T flip-flops A, B and C, and as few gates as possible. i. Write down the simplified SOP for TA, TB and TC (4 marks). ii. \( \quad \) Draw the circuit for this counter. Use as few gates as possible. (4 marks).