For the digital block shown in Figure. 2(a), the output Y=f(S₃,S₂,S₁,S₀) where S₃ is MSB and S₀ is LSB. Y is given in terms of minterms as $$Y\, = \,\sum m\left( {1,5,6,7,11,12,13,15} \right)$$ and its complements $$\overline Y \, = \,\sum m\left( {0,2,3,4,8,9,10,14} \right)$$.

(a) Enter the logical values in the given Karnaugh map [figure2(b)] for the output Y.
(b) Write down the expression for Y in sum-of products from using minimum number of terms.
(c) Draw the circuit for the digital logic boxes using four 2-input NAND gates only for each of the boxes.

The digital block in the figure is realized using two positive edge triggered D flip-flops. Assume that for t < t₀, Q₁ = Q₂ =0. The circuit in the digital block is given by

The 2’s complement representation of –17 is

For the ring oscillator shown in the figure, the propagation delay of each inverter is 100 pico sec. What is the fundamental frequency of the oscillator output?