(Solved): Design a 3-bit UP/DOWN counter that counts the bit sequence \( 0,2,4,6 \). Use positive edge trigg ...

Design a 3-bit UP/DOWN counter that counts the bit sequence \( 0,2,4,6 \). Use positive edge triggered \( \mathrm{JK} \) flip-flops and gates to implement the circuit. A control signal \( \mathrm{S} \) determines the mode of operation. \( \mathrm{S}=0 \), the counter acts as an UP counter. \( \mathrm{S}=1 \), the counter acts as a DOWN counter. The empty truth table columns are as follows. Simplified expression of \( \mathrm{K}_{\mathrm{C}} \) (i) \( K_{C}=S \) (ii) \( K_{C}=\bar{S} \cdot \overline{q_{B}}+\overline{q_{B}} \cdot S \) (iii) \( K_{C}=\bar{S} . q_{B}+\overline{q_{B}} . S \) (iv) \( K_{C}=0 \) or 1