title: Sequential circuit design
body: <p>A sequential circuit has two inputs, x1 and x2. Five-bit sequences  representing decimal digits coded in the 2-out-of-5 code appear from time to time on line a:,, synchronized with a clock pulse on a third line. Each five consecutive bits on the line x1, which occur while x2 = 0 but immediately following one or more inputs of x2 = 1, may be considered a code word. The single output z is to be 0, except upon the fifth bit of an invalid code word. Determine a state table of the above sequential circuit.
  2 out of 5 code</p>
  
  <ul>
  <li>0=00011 </li>
  <li>1=00101 </li>
  <li>2=00110 </li>
  <li>3=01001</li>
  <li>4=01010</li>
  <li>5=01100</li>
  <li>6=10001</li>
  <li>7=10010 </li>
  <li>8=10100  </li>
  <li>9=11000</li>
  </ul>
  
  <p>I have solved it with 16 states. could any one tell me the is it possible to reduces the number of states to less than 16?</p>