COE/EE 243Digital LogicSession 16; Page 1/3Spring 2003EE/CompE 243Quine-McCluskey Examples1. fabcd=∑m0345791113m00000 0 0000040 00 PIm30011 4 010045010 PIm40100 3 0011370 11 PIm50101 5 0101311011 PIm70111 9 1001513101 PIm91001 7 01115701 1PIm111011 11 101191110 1PIm131101 13 11019131 01 PIThe Prime Implicants are :a¼c¼d¼a¼bc¼a¼cd b¼cd bc¼da¼bd ab¼dac¼d2. fabcd=∑m245691011121315m20010 2 0010260 10 PI45121310 PIm40100 4 0100210010 PI41251310m50101 5 01014501091113151 1PIm60110 6 01104601 0 PI91311151 1m91001 9 1001412100m101010 10 1010513101m111011 12 110091110 1m121100 11 10119131 01m131101 13 11011011101 PIm151111 15 1111121311011151 11131511 1The Prime Implicants are :a¼cd¼b¼cd¼a¼bd¼ab¼cbc¼adCOE/EE 243Digital LogicSession 16; Page 2/3Spring 20033. fabcd∑m0345791113Use the Prime Implicants from problem 1.03457 91113Prime(0,4) a’c’d’ImplicantsEssentialXXXX NoXNo(3,11) b’cd XXXXXXX(9,13) ac’dNoNoNoNoXXXXNoYes(5,13) bc’d(5,7) a’bd(9,11) ab’d(3,7) a’cd(4,5) a’bc’fa¼c¼d¼ a¼cd ab¼d bc¼dORfa¼c¼d¼ ac¼d a¼bd b¼cd4. fabcd∑m245691011121315Use the Prime Implicants from problem 2PrimeImplicants(10,11) ab’c10 11 1215(2,6) a’cd’EssentialXXXXXXXXXYesYesNoNoNo24569 13XXNoXXXXX(9,11,13,15) ad(4,5,12,13) bc’(4,6) a’bd’(2,10) b’cd’fbc¼ ad a¼cd¼ b¼cd¼ORfbc¼ ad a¼cd¼ ab¼cORfbc¼ ad a¼bd¼ b¼cd¼COE/EE 243Digital LogicSession 16; Page 3/3Spring 20035. GABCDEF∑m123161718192632394863 ∑d152829301 000001 (1,3) 0000-1 (1,3,17,19) 0-00-1 PI2 000010 (1,17) 0-0001 (1,17,3,19) 0-00-116 010000 (2,3) 00001- (2,3,18,19) 0-001- PI32 100000 (2,18) 0-0010 (2,18,3,19) 0-001-———— (16,17) 01000- (16,17,18,19) 0100– PI3 000011 (16,18) 0100-0 (16,18,17,19) 0100–17 010001 (16,48) -10000 PI18 010010 (32,48) 100000 PI48 110000 ———————— (3,19) 0-001119 010011 (17,19) 0100-126 011010 (18,19) 01001-28 011100 (18,26) 01-010 PI———— ————29 011101 (26,30) 011-10 PI30 011110 (28,29) 01110- PI39 100111 PI (28,30) 0111-0 PI————63 111111 PI(63) ABCDEFPrimeImplicants 1231617181926 63Essential(26,30) A’BCEF’(28,29) A’BCDE’(28,30) A’BCDF’(16,17,18,19) A’BC’D’XXXXX XXXXXXXXXXYESYESNONONOYESYESNO39 4832XXXXXXNONOYES(2,3,18,19) A’C’D’E(1,3,17,19) A’C’D’F(18,26) A’BD’EF’(32,48) AC’D’E’F’(16,48) BC’D’E’F’(39) AB’C’DEF(a) GABCDEF AB¼C¼DEF AC¼D¼E¼F¼ A¼C¼D¼F A¼C¼D¼E A¼BC¼D¼