Logic Synthesis for AND-XOR-OR type Sense-Amplifying PLA

1. Logic Synthesis for AND-XOR-OR type Sense-Amplifying PLA Yoshida, H. Yamaoka, H. Ikeda, M. Asada, K. ASP-DAC 2002.and the 15th International Conference on VLSID 2002. Speaker 洪仲昀

3. Proposed synthesis flow Initial circuit Generate a candidate for a cube c Extract an XOR term Any other candidates? yes no Synthesis with extracted XOR terms Optimized circuit

4. Extraction of XOR Terms Let c = l1l2・ ・ ・ ln Thenfc⊆d ⊆ fl1fl2 … flnf⊇ c ♁d Ex: f = x1 x2 x4 + x1 x3 x4 + x2 x3 x4 + x2 x3 x4 let c=x1 x2 then fc =x3 x4 and fx1fx2 =x3 x4 so d=x3 x4 thus f contains x1 x2 ♁ x3 x4

5. Proof fc⊆d ⊆ fl1fl2…flnf⊇ c ♁d • fc⊆d ⊆ fl1fl2 … flnf⊇ c ♁d • f⊇ c ♁d f⊇ cd and f⊇ cd

6. Proof fc⊆d ⊆ fl1fl2…flnf⊇ c ♁d • Lemma A.1 fc⊇ df⊇ cd proof f⊇ c fc ⊇ cd ( f = cfc + cfc ) so fc⊇ d f⊇ cd fc⊇ d cofactor

7. Proof fc⊆d ⊆ fl1fl2…flnf⊇ c ♁d • Lemma A.2 c = l1l2・ ・ ・ ln f ⊇lk flk ⊇ lk fl1fl2 … fln (for any k) proof f⊇ (l1 +l2 +・ ・ ・ ln)fl1fl2 … fln = c fl1fl2 … fln ⊇ cd since c = l1l2・ ・ ・ ln we have f⊇ cd = l1d + l2d +・ ・ ・lnd flk⊇ d thus fl1fl2 … fln ⊇ d cofactor

8. Exact Method • Exact method uses all possible cubes as candidates • for cube c. form don’t care set

9. Prime implicants f = a`b`c` + a`b`c + ab`c + ab`c` + abc implicants: *01 1 10* 1 *00 1 00* 1 1*1 1 prime implicants: *0* 1 * 1*1 1 111 011 101 001 010 110 000 100

10. Covering problem 111 011 000 1 1 001 1 1 100 1 1 101 1 1 1 111 1 101 001 010 110 000 100