ions generating PN sequences. First, the individual sequences {an} have periods which are divisors of the desired period, and do not individu- ally have a "random appearance." Furthermore, very few of the input sequences change value at any one time, i.e., {a%} changes every 2i-th bit, thereby forcing the use of rather complicated logic to emulate a PN sequence which, on the average, changes every other bit. Example 5.2. The sequence 001100111010110111110 with period 21 has a particularly simple mechanization based on a shift reg- ister with feedback logic. Since all five-tuples (bm, bn+1, bn+2, bn+3, bn+4), n = 1,2, ,21, are distinct, it follows that bn+5 can be determined uniquely from these previous five symbols. Hence, the designer must find a simple Boolean function which mechanizes the mapping shown in Table 5.2. One possible result, employing GF(2) arithmetic, is (5.4) with the corresponding mechanization shown in Figure 5.3. Pseudonoise Generators Table 5.2 Feedback logic function The approach to determining the feedback function in Example 5.2 can be identical to that used in Example 5.1. The fact that Table 5.2 is incom- plete, i.e., the Boolean function's values are specified for only 21 of the 32 possible input binary 5-tuples, may yield some flexibility in the design process. Obviously, then, knowledge of the desired function in incomplete tabular form is not sufficient for determining the behavior of the PN gen- erator when its register is loaded with a 5-tuple not in the table. Using the b n +1 Figure 5.3. A shift-register generator using feedback logic. The Storage/Generation Problem implemented function (5.4), it can be seen that the device diagrammed in Figure 5.3 supports three other periodic sequences, namely 0 (period 1), 10000 (period 5), and 01010 (period 5). On the other hand, if the imple- mented function had the value 1 for each of the ten input 5-tuples missing from Table 5.2, the resulting device would support no other periodic sequences, and regardless of the initial register contents