JNTU B.Tech II DIGITAL LOGIC DESIGN Previous Question Paper (October - 2020 - R15)

Error detecting and correcting codes are redundant bits added to digital data to ensure reliable transmission and storage. Error detecting codes allow the receiver to determine if an error occurred during transmission, but they cannot identify the specific bit in error. Common examples include Parity bits, which add a single bit to make the total number of 1s even or odd, and Checksums or Cyclic Redundancy Checks (CRC), which use polynomial division to verify data integrity.

Error correcting codes go further by allowing the receiver to detect and automatically fix errors without retransmission. This is achieved by adding sufficient redundant bits to create a unique distance between valid code words, known as the Hamming distance. The most common example is the Hamming code, which uses multiple parity bits placed at power-of-two positions to identify and correct single-bit errors.

(i) Conversion of 68BE₁₆:

To convert Hexadecimal to Binary, replace each hex digit with its 4-bit binary equivalent: 6=0110, 8=1000, B=1011, E=1110. Thus, 68BE₁₆ = 0110100010111110₂.

To convert to Octal, group the binary digits into sets of three starting from the right: 011 010 001 011 111 0. Adding leading zeros gives 011 010 001 011 111 010, which corresponds to 321372₈.

(ii) Conversion of 345₁₀:

To convert to Binary, perform repeated division by 2: 345/2 = 172 R 1, 172/2 = 86 R 0, 86/2 = 43 R 0, 43/2 = 21 R 1, 21/2 = 10 R 1, 10/2 = 5 R 0, 5/2 = 2 R 1, 2/2 = 1 R 0, 1/2 = 0 R 1. Reading remainders from bottom to top: 101011001₂.

To convert to Hexadecimal, divide by 16: 345/16 = 21 R 9, 21/16 = 1 R 5, 1/16 = 0 R 1. Reading remainders from bottom to top: 159₁₆.