(Parity Checker Subsystem) The odd parity checker of Section 7.2.1 generates a 1 whenever a bit stream of serial inputs contains an odd number of 1s. This is useful in a data communication subsystem for checking that transmitted data has been sent correctly. Data is transmitted as 8 data bits appended with a ninth parity bit. The 9-bit sequence must be in odd parity. That is, if the data bits have an odd number of 1s, the parity bit is 0. If the data bits have an even number of 1s, the parity bit is 1. You are to design a parity checker that asserts OK if the 9-bit sequence is correct in odd parity and ERROR otherwise.
(a) Is it possible to write a state diagram with a small number of states to describe the behavior of this finite state machine? Does your state diagram need to track all possible sequences of 9 bits?
(b) Consider implementing the subsystem using the parity checker FSM of Figure 7.27 in conjunction with a synchronous 4-bit counter like the 163. Draw a schematic using logic gates, a single flip-flop, and the counter. Draw a timing diagram including a bit sequence that leads to ERROR and one that leads to OK.
