a) N binary-bits are used in the digital system representation to sample each analog signal, in this context, the digitized sample value can be given as:

D = b₀2⁰ + b₁2¹ + b₂2² + ··· + b_{N − 1}2^{N − 1}

Here, b₀, b₁, ..., b_{N − 1} denotes N bits and takes a value as 0 or 1. Recall that b0 is the least significant bit (LSB), 

and b_{N − 1} is the most significant bit (MSB). 

In this case, considering that D = b₃b₂b₁b₀ ‘is an analog signal ranging from 0 V to +15 V;
i) Find the corresponding D value for the given analog signal V_A = 0V, 1V, 2V, and 15V.
ii) Determine which value V_A will take will provide the change from 0 to 1 in b₀, b₁, b₂, b₃.
iii) What is the value of D when V_A = 5.2 V? Find the error?

b) Derive the Boolean expression for V_O in terms of V₁, V₂, V₃, V₄ in the given circuit. (Hint: Use logic gates.)

c) A diode circuit is given with the input signal V_i.

i) Find the output voltage by showing the complete solution step by step.
ii) Plot the V_O -V_i graph.

+Sv 10k +SV Vo Vsot