+The sequence in Problem 20 is a flag used in a communication network that represents the beginning of a message. This flag must be unique. As a consequence, at most five 1s in sequence may appear anywhere else in the message. Since this is unrealistic for normal message content, a trick called zero insertion is used. The normal message, which can contain strings of 1s longer than 5, enters input X of a sequential zero-insertion circuit. The circuit has two outputs, Z and S. When a fifth 1 in sequence appears on X, a 0 is inserted in the stream of outputs appearing on Z and the output S = 1, indicating to the circuit supplying the zero-insertion circuit with inputs that it must stall and not apply a new input for one clock cycle. This is necessary because the insertion of 0s in the output sequence causes it to be longer than the input sequence without the stall. Zero insertion is illustrated by the following example sequences

(a) Find the state diagram for the circuit

(b) Find the state table for the circuit and make a state assignment.

(c) Find an implementation of the circuit using D flip-flops and logic gates.

Problem 20

Repeat Problem 19 for the sequence 01111110 that is used in a different communication network protocol.

Problem 19

A Universal Serial Bus (USB) communication link requires a circuit that produces the sequence 00000001. You are to design a synchronous sequential circuit that starts producing this sequence for input E = 1. Once the sequence starts, it completes. If E = 1, during the last output in the sequence, the sequence repeats. Otherwise, if E = 0, the output remains constant at 1.

(a) Draw the Moore state diagram for the circuit.

(b) Find the state table and make a state assignment.

(c) Design the circuit using D flip-flops and logic gates. A reset should be included to place the circuit in the appropriate initial state at which E is examined to determine if the sequence of constant 1s is to be produced.