316
Digital Electronics
Ci
B
A
S
C o
Figure 9.15 Solution to problem 9.2 using a PLA.
Output 3 (less than)
= A 1 A 0 B 1 B 0 + A 1 A 0 B 1 B 0 + A 1 A 0 B 1 B 0 + A 1 A 0 B 1 B 0 + A 1 A 0 B 1 B 0 + A 1 A 0 B 1 B 0
(9.7)
Output 4 (greater than)
= A 1 A 0 B 1 B 0 + A 1 A 0 B 1 B 0 + A 1 A 0 B 1 B 0 + A 1 A 0 B 1 B 0 + A 1 A 0 B 1 B 0 + A 1 A 0 B 1 B 0
(9.8)
Figures 9.16(a) to (d) show the Karnaugh maps for the four outputs. The minimized Boolean
expressions can be written from the Karnaugh maps as follows:
Output 1equal to = A 1 A 0 B 1 B 0 + A 1 A 0 B 1 B 0 + A 1 A 0 B 1 B 0 + A 1 A 0 B 1 B 0
(9.9)
Output 2not equal to = A 1 B 1 + A 1 B 1 + A 0 B 0 + A 0 B 0
(9.10)