Consider the (7, 4) linear code whose parity-check matrix is 100 1011 Н- 010 1110 001 0111 a) Calculate the syndromes for the following error pattern e=0000001 (b) Determine the generator matrix (G c) Find the code word if the message m = 0011

Q1. Convert following numbers in given radix system: a. (697)10 into Octal and Hexa decimal b. (2D9)16 into Decimal and Octal Q2. Using two's complement representation, solve: a. 101110001 – 1111111001 b. 1010101010 – 1010010101 Q3. Perform following arithmetic operations: a. (6767)10 + (3592)10 using BCD b. (C7C)16 - (B0E)16 using 16's complement Q4. A code 1011011 needs to be sent to the receiver. Using, hamming code find out the code- word and the mechanism to check the corrected data when error occurred at 4th bit. (Assumptions: Right to Left with Odd Parity) Q5. (a) Convert the following logic gate circuit into a Boolean expression, writing Boolean sub-expressions next to each gate output in the diagram: A (b) Realise Ex-OR gate using universal gate? Q6. Implement and simplify f (A, B, C, D) = E(1,3,5,8,9,11,13,15) using K-map?

Design a code converter that converts a decimal digit from BCD to excess-3 code, the input variables are organized as (A BC D) respectively with A is the MSB, the output variables are organized as (W XY Z) respectively with W is the MSB, put the invalid decimal numbers as don't care. X= BCD'+B'D+B'C X= BC'D'+B'D+BC X= BC'D'+B'D+B'C X= BC'D'+BD+B'C

Design a counter that counts through all the oddnumbers from 0 to 7 and repeat when w=1; it countsthrough all the even numbers when w=0 and repeat. Use JKFFs