## Digital Logic Design & Analysis - May 2015

### Computer Engineering (Semester 3)

TOTAL MARKS: 80

TOTAL TIME: 3 HOURS
(1) Question 1 is compulsory.

(2) Attempt any **three** from the remaining questions.

(3) Assume data if required.

(4) Figures to the right indicate full marks.

** 1 (b) ** Represent (52_{10} into Excess-3 code and Gray code. (2 marks)

** 1 (c) ** Find the one's complement and two's complement of (57)_{10}. (2 marks)

** 1 (d) ** Realize y=AB+AB using NAND gates only. (2 marks)

** 1 (e) ** Obtain hamming code for 1011. (2 marks)

** 1 (f) ** Convert (126)_{10} to Octal, Hexcode. (2 marks)

** 1 (g) ** State demorgans law. (2 marks)

** 1 (h) ** Convert (214.32)_{10} to binary. (2 marks)

** 1 (i) ** Perform binary subtraction using 2's complement for (62)_{10} and (99)_{10}. (4 marks)

** 2 (a) ** Minimize the logic functon using Quine-McCluskey method.

f(A, B, C, D)=∑m(1, 3, 7, 9, 10, 11, 13, 15). (12 marks)

** 2 (b) ** Implement the following expression using single 4:1 Mux.

f=(A, B, C, D)= ∑m (0, 1, 2, 4, 6, 9, 12, 14). (8 marks)

** 3 (a) ** Design a 4-minute (A, B, C, D) digital circuit that will give at its output (X) a logic 1 only if the binary number at the input is between 2 and 9 (including). (10 marks)

** 3 (b) ** Simplify $$ Y = \overline {(A + \overline A B ) (C+ \overline D)} $$ (5 marks)

** 3 (c) ** Design 1 bit comparator using logic gates. (5 marks)

** 4 (a) ** Given the logic expression $$ A + \overline {BC} + AB\overline {D} + ABCD $$

i) Express on standard SOP

ii) Draw K-map for the equation.

iii) Minimize and realize using NAND gates only. (12 marks)

** 4 (b) ** Design 8 bit BCD adder. (8 marks)

** 5 (a) ** Design an mod-5 synchronous up counter using JK FF. (10 marks)

** 5 (b) ** Convert SR FF to TFF and JK FF. (10 marks)

### Write short note on (any three):

** 6 (a) ** VHDL. (7 marks)

** 6 (b) ** Multivibrators (7 marks)

** 6 (c) ** Gray code & Excess - 3 code(7 marks)

** 6 (d) ** Johnson Ring Counter. (7 marks)

**1 (a) ** Convert (121.2)_{3} into base 10. (2 marks)