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A binary $3$-bit down counter uses $J$-$K$ flip-flops, $FF_{i}$ with inputs $J_{i}$, $K_{i}$ and outputs $Q_{i}$, $i$ = $0, 1, 2$ respectively. The minimized expression for the input from following is :

  1. $J_{0} = K_{0} = 0$
  2. $J_{0} = K_{0} = 1$
  3. $J_{1} = K_{1} = Q_{0}$
  4. $J_{1} = K_{1} = \overline{Q}_{0}$
  5. $J_{2} = K_{2} =Q_{1} Q_{0}$
  6. $J_{2} = K_{2} =\overline{Q}_{1} \overline{Q}_{0}$
  1. I, III, V
  2. I, IV, VI
  3. II, III, V
  4. II, IV, VI
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