$($a$)$ Design a counter with three LM flip$-$flops that goes through the following binary repeated

sequence: $(000$ treating transitions out of other states as

don't cares. LM flip$-$flop operation is described in the table below. You are only allowed to use

LM flip$-$flops and no other.gates. $(15$ pts$)0000010111110100,000$

$($b$)$ Based on$\text{'}$ this design, show what happens when the counter enters the binary states $010$ and

$101$ accidentaly, by drawing the sequence of states encounterd from there on$.(5$ pts$)$