1. Boolean Algebra for CAD Applications
Shmuel Wimer
Bar Ilan Univ., School of Engineering

2. Binary Decision Diagram – BDD
Set one variable at a each level of tree
Index=1
Index=2
Index=3
Evaluate function at leaves
BDD
OBDD b a 1 c a 1 c 1 1 b 1 1

3. Binary Decision Diagram – OBDD

4. OBDD Isomorphism and Redundancy

5. Reduced OBDD – ROBDD 1 b a c
OBDD b a 1 c
ROBDD

6. Bottom-up ROBDD Generation

8. 1 b a c OBDD ROBDD a b 1 c 1 <4,3> Id=5 Id=5 <1,3> Id=4b a c
OBDD
ROBDD
<4,3>
Id=5 a 1
Id=5
<1,3>
Id=4
<3,3>
Id=3 b 1
Id=4
<1,2>
Id=3
<1,2>
Id=3 1 c
Id=3 1
Id=1
Id=2
Id=1
Id=2

9. ROBDD Construction with ITE Operator
Instead of reducing OBDD, ROBDD can be constructed

11. a: 1 a b: 1 b c: 1 c 1 c
ac+bc: b a 1 c
ac: a 1 c
bc: b

12. ITE Algorithm

13. ITE Applications