600 CHAPTER 12 / MODULE AND BIT-SLICE DEVICES
Eq. (12.10),
D
A
= (
¯
A
¯
B
¯
C ) ⊕C ⊕ D = D ⊕ (
¯
A
¯
B + C),
in literal form, which can be proved by applying the laws of XOR algebra in Section 3.11.
A cursory inspection of Eq. (12.12) and Table 12.1 indicates that the maximum number
of XOR operations is three, independent of ALFSR counter size, but only after simplifying
by application of Eqs. (3.25) and (3.13). Fortunately, three XOR operations can be handled
very easily by a standard four-input, even-parity generator module such as that in Fig. 6.32c.
The problem is, of course, in dealing with the large number of ANDed complements present
in the correction functions. If CMOS logic is permitted, the multiple input NOR gate in
Figure 8.46 can be used to great ...