1. ECE 465 PLA Optimization Using Modified Multi-Function QM
Shantanu Dutt
ECE Dept.
University of Illinois at Chicago
Acknowledgement: Powerpoint slide & solution to magnitude comparator problem given here (next 5 slides) prepared by Sajjad Rahaman in consultation with Prof. Dutt

2. 2-bit Magnitude Comparator
EQ does not share any MT with other o/p functions. So, only NE, LT, and GT will be considered in the multiple-function QM optimizer

3. PI Formation Min term List 1 List 2 List 3 Flag 1 0000 αβ √ 1,3 00_1
1,3,9,11
_0_1 α
PI1 2
0010
1,9
_001
PI13
2,3,6,7
0_1_
PI2 4
0100 αγ
2,3
001_
4,6,12,14
_1_0
PI3 8
1000
2,6
0_10
PI12
8,9,12,13
1_0_
PI4 3
0011
4,6
01_0 6
0110
4,12
_100
PI11 9
1001
8,9
100_ 12
1100
8,12
1_00
PI10 7
0111
3,7
0_11
PI9 11
1011
3,11
_011
PI8 13
1101
6,7
011_ 14
1110
6,14
_110
PI7
9,11
10_1
9,13
1_01
PI6
12,13
110_
12,14
11_0
PI5

4. Min-Cost Covering: PI Table
Using a PI w/ fewer literals does not reduce PI cost for PLA optimization
Thus each PI cost should be 1
Min-Cost Covering: PI Table fα fβ fγ
cost
Flag 1 2 3 4 6 7 8 9 11 12 13 14
PI1 α √
PI2 αβ
PI3
PI4 αγ
PI5
PI6
PI7
PI8
PI9
PI10
PI11
PI12
PI13
PI14 *1 *3 *2 *4

5. Min-Cost Covering: Reduced PI Tablefα fβ fγ
cost
Flag 2 6 7 8 9 13 1
PI1 α √
PI2 αβ
PI3
PI4 αγ
PI6
PI7
PI9
PI10
PI12
PI13 1 C
* 9 C 4
* 10 2 5 6 3 7 8

6. 2-bit Magnitude Comparator: Final Solution
Total AND gate needed for PLA = 6+4=10
compared to 12 AND gates if each o/p function is minimized individually
Side Note: Since EQ = NE, no AND lines need be used in the PLA for generating the 4 MTs of EQ. NE can be complemented to generate EQ