CSIT-304 - Digital Circuits & System (DSC)

Given the following Boolean function : F(W,X,Y,Z) = WX'(Y + Z') + X'.Z'(W'Y) where \Theta represents the XNOR operation, determine the simplified(minimal) SOP expression for F using boolean algebra and Implement the given function using NOR-NOR logic. [7 Marks]

Computer the prime implicants (PI) and essential prime implicants (EPI) in the following Boolean function $F(W, X, Y, Z) = \Sigma M(1, 3, 5, 7, 8, 9, 11, 12) + d(2, 10)$ Computer a minimal SOP expression for F and determine whether it is unique. [7 Marks]

Each of the following functions actually represents a set of four functions, corresponding to the possible assignments of the don't-care terms. $f_1(w,x,y,z)=\Sigma(1,3,5,6,9,10)+\Sigma(11,12)$ $f_2(w,x,y,z)=\Sigma(0,3,4,5,8,9)+\Sigma(6,7)$

i) Find $f_1=f_2$. How many functions does $f_1$ represent?

ii) Find $f_1+f_2$. How many functions does $f_4$ represent? [7 Marks]

Given the network of fig., determine the functions $f_1$ and $f_2$ if $f_1 = xz + x'z'$ and the overall transmission function is to be $f(w,x,y,z) = \Sigma(0,3,6,10,11,12)$ alt='' [7 Marks]

Design a $8 \times 1$ multiplexer using one $4 \times 1$ multiplexer and four $2 \times 1$ multiplexers. [7 Marks]

Design a combinational logic circuit to convert the BCD to excess-3 code. [7 Marks]

Design a $3 \times 8$ decoder using one $2 \times 4$ decoder and two $2 \times 4$ decoder with Enable input. [7 Marks]

Draw a schematic for a minimal circuit that uses only NOR gates that performs the two's complement operation on a four bit input value. Let the input be $A_3A_2A_1A_0$ and the output be $B_3B_2B_1B_0$. [7 Marks]

Covert Decimal to Binary

i) (1024)$_{10}$

ii) (23.25)$_{10}$ [7 Marks]

Draw the state diagram for the following specification sequential systems: Input: $x(t) \in \{0,1\}$ Output: $z(t) \in \{0,1\}$ State: $s(t) \in \{\text{Even, Odd}\}$ Initial state: $s(0) = \text{Even}$ Functions: The transition and output functions are $s(t+1) = \text{even if } x(t) \text{ and } y(t) \text{ both are even}$ $s(t+1) = \text{odd otherwise}$ $z(t) = 1 \text{ if } x(t) \text{ and } y(t) \text{ both are even}$ $z(t) = 0 \text{ otherwise}$ alt='' [7 Marks]

Design a synchronous counter to count in the random sequence 0, 2, 4, 5, 7, 0, 2, 4, 5, 7, ... using D flip-flop. [7 Marks]

Design a sequential circuit using T flip-flop for the following state table.

Explain Interfacing between TTL and MOS with example. [7 Marks]

Explain the concept of working and applications of following memories.

i) ROM

ii) PLA

iii) DRAM

iv) FLASHRAM [7 Marks]

i) A/D and D/A convertors [14 Marks]

ii) CMOS Logic [14 Marks]

iii) Shannon's theorem for channel capacity [14 Marks]

iv) Nyquist sampling theorem [14 Marks]