Circuit desgin Nd maths

Task A - Design a finite state machine to implement the following sequence detector. 35% A synchronous sequential circuit having a single input x and a single output z is to be designed. The output z is to become 1 upon completion of the input sequence 0101, whether it forms part of an overlapping string (such as 00010101) or not. (a) Construct a state diagram. (10 Marks) (b) Construct an appropriate state assignment map. (3 Marks) (c) Assume the use of JK flip-flops and construct a transition table. (5 Marks) (d) Construct excitation and output Boolean functions. (6 Marks) (e) Draw the diagram of the resulting circuit. (3 Marks) (f) Repeat parts c, d, and e but with D flip-flops. Compare the complexity of the circuits. (8 Marks) Task B – Using a Mealy machine to design a circuit for the problem – 35% A sequential circuit is to be designed having a single input line x and a single output line z. Starting in a reset state, the circuit receives input sequences consisting of 3-bit binary words. Each input word follows the preceding word with a delay of one clock period. The circuit must be in the reset state at the beginning of each word. The output is to be z = 1 upon receipt of the third bit of a word if the total number of level changes (from 0 to 1 or from 1 to 0) is odd (101, for example, has two level changes while 001 has only one). Such a circuit is called a change-of-level detector. Please design a Mealy machine for this detector. You need to provide the detailed design process. (a) The state diagram (15 Marks) (b) The state transition table and derivation of Boolean functions (12 Marks) (c) The circuit diagram, and a brief description of its functions (8 Marks) Task C – Design Challenge – 30% A synchronous sequential circuit is to have three inputs: A, B, and [login to view URL] single output z is to be 0 except for the following possible inputs: z = 1 when C = 0 and A and B had identical values two clock periods earlier. z = 1 when C = 1 and A and B had opposite values three clock periods earlier. Obtain an implementation of the circuit and discuss its nature. (a) Analyse the problem, provide the state diagram, state transition table. (12 Marks) (b) Derive the Boolean functions, and draw the circuit diagram. (10 Marks) (c) A discussion of the design (including what is the machine type of your choice, how your design meets the requirements, etc.). (8 Marks)