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Step 1 of 1 2.034E The traffic-light controller of Table 2-12 in the textbook contains 6 code words to represent different states in the traffic-light controller. Usually for a system with n bits it is possible to encode 2" states. Hence by means of 3 bits there are (that is 8) encode states possible. Consider that every state must be encoded with at least one zero in the code word to save power. So out of the eight states use only seven states leaving the 111 state. As our traffic system needs only 6 states, we can have more than one possible way of state encoding. Use the following combinational formula to find the combinations. (1) Here, The following is the total number of states that have at least one zero in its code word. (except 111 state) =8-1 = 7 The required number of states for the traffic system, Substitute 7 for n and 6 for r in equation (1). = = 7 Hence, 7 different ways of assigning 6 three-bit binary state encodings are possible.