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Quine Mc Clusky (Tabular) method
- 1. EXAMPLE: Simplify the Boolean Expression using Quine McClusky method (Tabular Method) )15,11,9,8,7,3,1,0(),,,( mDCBAF 1 DR. SYED HASAN SAEED, INTEGRAL UNIVERSITY, LUCKNOW
- 2. CONVERT DECIMAL NUMBERS TO BINARY NUMBERS DECIMAL NUMBER EQUIVALENT BINARY NUMBER MINTERMS 0 0000 m0 1 0001 m1 3 0011 m3 7 0111 m7 8 1000 m8 9 1001 m9 11 1011 m11 15 1111 m15 2 DR. SYED HASAN SAEED, INTEGRAL UNIVERSITY, LUCKNOW
- 3. STEP 1: Arrange all Minterms according to number of 1 as shown in table 2 STEP: 2 Compare each minterm in group ‘n’ with each minterm in group (n+1) and identify the match pairs. A match pair is a pair of minterms which differ only in one variable. For the variables differ place (-) dash, as shown in Table 3 3 DR. SYED HASAN SAEED, INTEGRAL UNIVERSITY, LUCKNOW
- 4. Group Minterm No. IN BINARY A B C D 0 0 0 0 0 0 1 1 0 0 0 1 8 1 0 0 0 2 3 0 0 1 1 9 1 0 0 1 3 7 0 1 1 1 11 1 0 1 1 4 15 1 1 1 1 TABLE : 2 STEP 3: Now compare all the pairs of minterms of table 3 with those in the adjacent groups. As shown in table 4 4 DR. SYED HASAN SAEED, INTEGRAL UNIVERSITY, LUCKNOW
- 5. Group Minterm No. IN BINARY A B C D 0 0 0 0 0 0 1 1 0 0 0 1 8 1 0 0 0 2 3 0 0 1 1 9 1 0 0 1 3 7 0 1 1 1 11 1 0 1 1 4 15 1 1 1 1 TABLE : 3 Group Minterm No. IN BINARY A B C D 0 (0,1) 0 0 0 - (0,8) - 0 0 0 1 (1,3) 0 0 - 1 (1,9) - 0 0 1 (8,9) 1 0 0 - 2 (3,7) 0 - 1 1 (3,11) - 0 1 1 (9,11) 1 0 - 1 3 (7,15) - 1 1 1 (11,15) 1 - 1 1 TABLE : 2 STEP 3: Now compare all the pairs of minterms of table 3 with those in the adjacent groups. As shown in table 4 5 DR. SYED HASAN SAEED, INTEGRAL UNIVERSITY, LUCKNOW
- 6. Group Minterm No. IN BINARY A B C D 0 0 0 0 0 0 1 1 0 0 0 1 8 1 0 0 0 2 3 0 0 1 1 9 1 0 0 1 3 7 0 1 1 1 11 1 0 1 1 4 15 1 1 1 1 TABLE : 3 Group Minterm No. IN BINARY A B C D 0 (0,1) 0 0 0 - (0,8) - 0 0 0 1 (1,3) 0 0 - 1 (1,9) - 0 0 1 (8,9) 1 0 0 - 2 (3,7) 0 - 1 1 (3,11) - 0 1 1 (9,11) 1 0 - 1 3 (7,15) - 1 1 1 (11,15) 1 - 1 1 Group Minter mNo. IN BINARY A B C D 1 0,1,8,9 - 0 0 - 0,8,1,9 - 0 0 - 2 1,3,9,11 - 0 - 1 1,9,3,11 - 0 - 1 3 3,7,11,15 - - 1 1 3,11,7,15 - - 1 1 TABLE : 2 TABLE : 4 STEP 3: Now compare all the pairs of minterms of table 3 with those in the adjacent groups. As shown in table 4 6 DR. SYED HASAN SAEED, INTEGRAL UNIVERSITY, LUCKNOW
- 7. GROUP MINTERMS BINARY REPRESENTATION A B C D 1 m0-m1-m8-m9 - 0 0 - m0-m8-m1-m9 - 0 0 - 2 m1-m3-m9-m11 - 0 - 1 m1-m9-m3-m11 - 0 - 1 3 m3-m7-m11-m15 - - 1 1 m3-m11-m7-m15 - - 1 1 TABLE: 5 STEP: 4 Repeat the procedure for grouping. If can group the Quads of minterms in the adjacent groups of table 4 to obtain groups of eight minterms. There are no such matching. Now prepare Prime Implicant Table as shown in Table 5 B D CD B C 7 DR. SYED HASAN SAEED, INTEGRAL UNIVERSITY, LUCKNOW
- 8. PI Minterms group & Boolean representation GIVEN MINTERMS 0 1 3 7 8 9 11 15 √ (0,1,8,9) X X X X (1,3,9,11) X X X X √ (3,7,11,15) X X X X √ √ √ √ √ √ √ √ TABLE: 6 From table 6 Essential Prime Implicants are B C and CD Required Output BY C CD CB DB DC 8 DR. SYED HASAN SAEED, INTEGRAL UNIVERSITY, LUCKNOW