Boolean Function SOP & POS

Boolean Function

1. Boolean Function Dr. (Mrs.) Gargi Khanna Associate Professor Electronics & Communication Engineering Department National Institute of Technology, Hamirpur

2. Boolean function A Boolean function has: At least one Boolean variable, At least one Boolean operator, and At least one input from the set {0,1}. It produces an output that is also a member of the set {0,1}.

3. Truth Table Addition of 2 bits: A B Sum Carry 1 1 1 1 1 1 1 Sum     Sum    

4. Truth Table Subtraction of 2 bits: A B Difference Borrow 1 1 1 1 1 1 1 Difference       A’ +B’)  

5. Truth Table Addition of 3 bits: A B C Sum Carry 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 Sum   ABC   Sum  

6. Two-Level Implementations Boolean functions in either SOP or POS forms can be implemented using 2-Level implementations. For SOP forms AND gates will be in the first level and a single OR gate will be in the second level. For POS forms OR gates will be in the first level and a single AND gate will be in the second level. SOP forms can be implemented using only NAND gates, while POS forms can be implemented using only NOR gates.

7. F = XZ + Y’Z + X’YZ XZ Y’Z X’YZ XZ . Y’Z . X’YZ = XZ + Y’Z + X’YZ F = XZ + Y’Z + X’YZ

8. Implement the following POS function F = (X+Z) (Y’+Z) (X’+Y+Z)

9. Standard SOP Write minterms of BC + A. Solution : BC + A Write terms XBC + A XX Add Xs where letters are missing A’BC , ABC Vary X s in XBC AB’C’, AB’C, ABC’, ABC Vary Xs in AXX Thus BC + A = A’ BC +ABC+ AB’C’ + AB’C + A B C’ + A B C or BC + A = A’BC + ABC + AB’C’ + AB’C + ABC’

10. Standard SOP F(A.B,C) = Σ m(3, 7, 4, 5, 6)

11. Complementary Nature of Min & Max terms

12. F= Σ m( 15, 11, 14, 13, 12) F= П M (0,1,2,3,4,5,6,7,8,9,10 )

13. Standard POS Write full form of the expression Y(A,B,C) = П M (0 , 1, 3, 4)

14. Standard SOP & POS F= B ’+A’C X0X, 0X1 (000 , 001,100,101), (001,011) F= Ʃm (0,1,4,5,3,8) F(A,B,C)=(A+B)(A’+C) (0+0+X) (1+X+0)=(0+0+0),(0+0+1),(1+0+0),(1+1+0) F= П M(1,0,4,6 )

15. Happy Learning