Question 2751 – UGC NET CS 2017 Jan -paper-2

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
I. J​ ₀​ = K​ ₀​ = 0
II. J​ ₀​ = K​ ₀​ = 1
III. J​ ₁​ = K​ ₁​ = Q​ ₀
IV. J​ ₁​ = K​ ₁​ =Q’₀
V. J​ ₂​ = K​ ₂​ = Q​ ₁​ Q​ ₀
VI. J​ ₂​ = K_{​ 2}​ = Q’​ ₁​ Q’_{​ 0}

Correct Answer: D

In a JK flip-flop, Q_n=Q(bar) iff J=K=1.
State sequence of down counter is as follows: