Mathematical Foundation of Computer Science

DHARM N-COM\APPENDIX.PM5 364 MATHEMATICAL FOUNDATION OF COMPUTER SCIENCE = (p′ + q + r)(p′ + q + r′)(p + q + r)(p + q + r′)(p + ...

DHARM N-COM\APPENDIX.PM5 BOOLEAN ALGEBRA 365 = (x + y′) (x′ + 0) (0 + y) P1 = (x + y′) (x′ + y y′) (x x′ + y) P2 = (x + y′) (x′ ...

DHARM N-COM\APPENDIX.PM5 366 MATHEMATICAL FOUNDATION OF COMPUTER SCIENCE = (x x + z x + x y′ + z y′) (x′ + y) P4 = (x + x z + x ...

DHARM N-COM\APPENDIX.PM5 BOOLEAN ALGEBRA 367 y′ yyy′ x′ x′ xx ()a ()b 111 1 Fig. A.9 Consider another example, f 2 (x, y) = x + ...

DHARM N-COM\APPENDIX.PM5 368 MATHEMATICAL FOUNDATION OF COMPUTER SCIENCE Similarly K-map of 4 variables consists of 16 (= 2^4 ) ...

DHARM N-COM\APPENDIX.PM5 BOOLEAN ALGEBRA 369 in the K-map are so arranged that the adjacent cells are differs only by a single v ...

DHARM N-COM\APPENDIX.PM5 370 MATHEMATICAL FOUNDATION OF COMPUTER SCIENCE wx yz or or or Fig. A.16 Example 5.7. Simplify the K-ma ...

DHARM N-COM\APPENDIX.PM5 BOOLEAN ALGEBRA 371 wx yz 11 11 11 111 0 0 00 00 0 Fig. A.18 f(x, y, z) = (w + x + y′) (w + x′ + y)(x′ ...

DHARM N-COM\APPENDIX.PM5 372 MATHEMATICAL FOUNDATION OF COMPUTER SCIENCE Further, these expression lies on the adjacent edges so ...

DHARM N-COM\APPENDIX.PM5 BOOLEAN ALGEBRA 373 That can be represented by the K-map shown in Fig. A.22. pq rs pq′′ pq′ pq pq′ rs′ ...

DHARM N-COM\APPENDIX.PM5 374 MATHEMATICAL FOUNDATION OF COMPUTER SCIENCE Since, no more 0 left in the K-map for consideration, t ...

DHARM N-COM\APPENDIX.PM5 BOOLEAN ALGEBRA 375 To obtain X 1 and X 2 in PoS, combing 0’s so we get the complement of the function ...

DHARM N-COM\APPENDIX.PM5 376 MATHEMATICAL FOUNDATION OF COMPUTER SCIENCE A.5 Using K-map representation find the minimal CNF exp ...