Question 5 a) A method of increasing hardware performance is to incorporate pipelining. ) Sketch the circuit block diagram for an un-pipelined and a pipelined digital i) If multiplier circuitry has a propagation delay of 9ns and addition/subtraction ii) Circuit that will read three data inputs x, y and z and output the result (x3 + 6xz-3y). (5 marks) (4 marks) (3 marks) circuitry 4ns, determine the latency and maximum input freqency of the two circuit structures developed in i). Briefly discuss the issues associated with increasing the number of pipeline stages in complex circuitry. b) A Hamming error coding system comprises of a transmitter (TX) and a receiver (RX). The X encodes 4 data bits (bi to ba) into 7 bit codes (c1 to c7), before transmitting to the RX. Where C1 C4b1 b4 c6 b1 b3 b4 c7 b2 b3 b4 i) Demonstrate, why the above Hamming code is known as a perfect i) Derive the Boolean functions for the three parity bits in the RX, used to and determine the efficiency of the code. (4 marks) determine whether a received code has been corrupted by noise. Using the parity functions determine the original encoded data transmitted by the TX if the code 1000101B was received at the RX. (9 marks) Question 5 a) A method of increasing hardware performance is to incorporate pipelining. ) Sketch the circuit block diagram for an un-pipelined and a pipelined digital i) If multiplier circuitry has a propagation delay of 9ns and addition/subtraction ii) Circuit that will read three data inputs x, y and z and output the result (x3 + 6xz-3y). (5 marks) (4 marks) (3 marks) circuitry 4ns, determine the latency and maximum input freqency of the two circuit structures developed in i). Briefly discuss the issues associated with increasing the number of pipeline stages in complex circuitry. b) A Hamming error coding system comprises of a transmitter (TX) and a receiver (RX). The X encodes 4 data bits (bi to ba) into 7 bit codes (c1 to c7), before transmitting to the RX. Where C1 C4b1 b4 c6 b1 b3 b4 c7 b2 b3 b4 i) Demonstrate, why the above Hamming code is known as a perfect i) Derive the Boolean functions for the three parity bits in the RX, used to and determine the efficiency of the code. (4 marks) determine whether a received code has been corrupted by noise. Using the parity functions determine the original encoded data transmitted by the TX if the code 1000101B was received at the RX. (9 marks)