204:. Compared to the other methods, this one is essentially more efficient, reducing memory usage and computation time by several orders of magnitude. Its name reflects the way of instantly making a cup of fresh coffee. There is hardly any restriction to the number of variables, output functions and product terms of a combinational function block. In general, e.g. tens of variables with tens of output functions are readily dealt with.
103:
Digit Code
Segments A B C D E F G 0 0000 1 1 1 1 1 1 0 -A- 1 0001 0 1 1 0 0 0 0 | | 2 0010 1 1 0 1 1 0 1 F B 3 0011 1 1 1 1 0 0 1 | | 4 0100 0 1 1 0 0 1 1 -G- 5
135:
is a laborious, tedious and error prone process. It isn't suited for more than six input variables and practical only for up to four variables, while product term sharing for multiple output functions is even harder to carry out. Moreover, this method doesn't lend itself to be automated in the form
95:
The starting point for the design of a digital logic circuit is its desired functionality, having derived from the analysis of the system as a whole, the logic circuit is to make part of. The description can be stated in some algorithmic form or by logic equations, but may be summarized in the form
291:
program that provides a graphical interface to
Espresso, as well as to misII, another module in the Berkeley Octtools package. With Logic Friday users can enter a logic function as a truth table, equation, or gate diagram, minimize the function, and then view the results in both of the other two
207:
The input for ESPRESSO is a function table of the desired functionality; the result is a minimized table, describing either the ON-cover or the OFF-cover of the function, depending on the selected options. By default, the product terms will be shared as much as possible by the several output
136:
of a computer program. However, since modern logic functions are generally not constrained to such a small number of variables, while the cost as well as the risk of making errors is prohibitive for manual implementation of logic functions, the use of computers became indispensable.
175:
with the number of variables. A similar problem occurs when increasing the number of output functions of a combinational function block. As a result, the Quine–McCluskey method is practical only for functions with a limited number of input variables and output functions.
170:
is very well suited to be implemented in a computer program, the result is still far from efficient in terms of processing time and memory usage. Adding a variable to the function will roughly double both of them, because the truth table length increases
327:
as an additional optimization technique for the various algorithms in ESPRESSO-II that are based on the unate recursive paradigm. Another addition is allowing control over when literals can be raised which can be exploited to effectively minimize
84:
circuits. Since memory elements are standard logic circuits they are selected out of a limited set of alternative circuits; so designing digital functions comes down to designing the combinational gate circuits and interconnecting them.
195:
Rather than expanding a logic function into minterms, the program manipulates "cubes", representing the product terms in the ON-, DC-, and OFF- covers iteratively. Although the minimization result is not guaranteed to be the
303:
is a free
Windows program that provides logic minimization exploiting this Espresso algorithm. It is able to generate a two-level gate implementation for a combinational function block with up to 40 inputs and outputs or a
114:
Next, the minimized result may be split up in smaller parts by a factorization procedure and is eventually mapped onto the available basic logic cells of the target technology. This operation is commonly referred to as
104:
0101 1 0 1 1 0 1 1 | | 6 0110 1 0 1 1 1 1 1 E C 7 0111 1 1 1 0 0 0 0 | | 8 1000 1 1 1 1 1 1 1 -D- 9 1001 1 1 1 1 0 1 1
223:
tool. For implementing a function in multi-level logic, the minimization result is optimized by factorization and mapped onto the available basic logic cells in the target technology, whether this concerns a
43:
by Robert K. Brayton et al. in 1982. and improved as ESPRESSO-II in 1984. Richard L. Rudell later published the variant ESPRESSO-MV in 1986 and ESPRESSO-EXACT in 1987. Espresso has inspired many derivatives.
92:, which can be carried out by hand, but usually some formal method by computer is applied. In this article the design methods for combinational logic circuits are briefly summarized.
208:
functions, but the program can be instructed to handle each of the output functions separately. This allows for efficient implementation in two-level logic arrays such as a
799:
52:
Electronic devices are composed of numerous blocks of digital circuits, the combination of which performs the required task. The efficient implementation of
276:(.deb) file format as well the C source code. The last release was version 9.0 dated 2008. A Windows and C++20 compatible was ported to GitHub in 2020.
219:
The ESPRESSO algorithm proved so successful that it has been incorporated as a standard logic function minimization step into virtually any contemporary
100:
driver that translates the binary code for the values of a decimal digit into the signals that cause the respective segments of the display to light up.
60:
circuits (such that no more logic gates are used than are necessary) is necessary to minimize production costs, and/or maximize a device's performance.
111:
phase, to be described below, in order to simplify the function table by combining the separate terms into larger ones containing fewer variables.
163:
is composed. Finally, a systematic procedure is followed to find the smallest set of prime implicants the output functions can be realised with.
966:
415:
563:
697:
385:(1982). "A comparison of logic minimization strategies using ESPRESSO: an APL program package for partitioned logic simulation".
349:
229:
981:
558:
514:
444:
382:
939:
828:
794:
481:
Bolton, Martin (1990). "4.3.3 ESPRESSO-II". Written at
University of Bristol, Bristol, UK. In Dagless, Erik L. (ed.).
411:
254:
185:
976:
971:
949:
736:
705:
667:
634:
496:
462:
365:
789:
626:
329:
488:
225:
184:
A different approach to this issue is followed in the ESPRESSO algorithm, developed by
Brayton et al. at the
167:
454:
869:
155:
for which the functions are active (the ON-cover) or for which the function value is irrelevant (the
659:
603:
250:
213:
209:
140:
69:
536:
407:
374:
440:
156:
88:
In general the instantiation of logic circuits from high-level abstraction is referred to as
753:
305:
172:
8:
758:
618:
144:
81:
73:
200:, in practice this is very closely approximated, while the solution is always free from
722:
652:
580:
482:
434:
432:
273:
116:
323:
is a JavaScript implementation of ESPRESSO-II for single output functions. It employs
188:. It is a resource and performance efficient algorithm aimed at solving the heuristic
945:
935:
732:
701:
691:
687:
683:
663:
630:
510:
502:
492:
458:
361:
288:
97:
584:
429:
763:
572:
324:
201:
139:
The first alternative method to become popular was the tabular method developed by
128:
381:
Brayton, Robert King; Hachtel, Gary D.; Hemachandra, Lane A.; Newton, A. Richard;
931:
220:
160:
89:
754:
Fast
Heuristic and Exact Algorithms for Two-Level Hazard-Free Logic Minimization
448:
357:
197:
189:
53:
898:
576:
960:
820:
728:
561:(September 1987). "Multiple-valued logic minimization for PLA optimization".
438:
387:
Proceedings of the IEEE International
Symposium on Circuits and Systems, 1982
265:(equation to truth table) program, an updated version of ESPRESSO for modern
132:
77:
408:"Robert K. Brayton; Professor Emeritus, Professor in the Graduate School"
148:
96:
of a table as well. The below example shows a part of such a table for a
924:
Funktionaler
Entwurf digitaler Schaltungen - Methoden und CAD-Techniken
849:
57:
36:
32:
768:
487:. Electronic Systems Engineering Series (1 ed.). Wokingham, UK:
28:
24:
16:
Computer program for complexity reduction of digital logic circuits
928:
Functional design of digital circuits - Methods and CAD techniques
550:
292:
representations. The last release was version 1.1.4 dated 2012.
152:
506:
903:
854:
453:(9th printing 2000, 1st ed.). Boston, Massachusetts, USA:
380:
270:
68:
All digital systems are composed of two elementary functions:
556:
266:
257:
website. The last release was version 2.3 dated 1988. The
390:
80:, like counters, are a combination of memory elements and
877:
850:"Espresso heuristic logic minimizer C++20 Windows source"
40:
821:"Espresso-eb / eqntott C source code and program (2008)"
402:
400:
537:"Multiple-Valued Logic Minimization for PLA Synthesis"
397:
63:
651:
122:
39:circuits. ESPRESSO-I was originally developed at
958:
450:Logic Minimization Algorithms for VLSI Synthesis
891:
745:
151:for a set of logic functions, by combining the
751:
623:Synthesis and Optimization of Digital Circuits
484:Digital Systems Design with Programmable Logic
782:
752:Theobald, Michael; Nowick, Steven M. (1998).
682:
476:
474:
862:
842:
192:-free two-level logic minimization problem.
813:
611:
921:
724:Practical Digital Logic Design and Testing
643:
617:
591:
564:IEEE Transactions on Computer-Aided Design
528:
471:
767:
714:
676:
559:Sangiovanni-Vincentelli, Alberto Luigi M.
445:Sangiovanni-Vincentelli, Alberto Luigi M.
383:Sangiovanni-Vincentelli, Alberto Luigi M.
342:
308:with up to 256 states. It is part of the
107:The implementation process starts with a
698:The Benjamin/Cummings Publishing Company
439:Brayton, Robert King; Hachtel, Gary D.;
230:application-specific integrated circuit
959:
930:]. Springer-Lehrbuch (in German).
597:
534:
480:
967:Electronic design automation software
649:
348:
179:
720:
13:
915:
795:University of California, Berkeley
412:University of California, Berkeley
315:
255:University of California, Berkeley
186:University of California, Berkeley
14:
993:
922:Eschermann, Bernhard (May 1993).
598:Rudell, Richard L. (April 1989).
535:Rudell, Richard L. (1986-06-05).
76:that transform that information.
212:(Programmable Logic Array) or a
64:Designing digital logic circuits
831:from the original on 2018-09-21
802:from the original on 2018-09-21
790:"Espresso C source code (1988)"
627:McGraw-Hill Science Engineering
600:Logic Synthesis for VLSI Design
418:from the original on 2018-09-23
279:
168:Quine–McCluskey algorithm
47:
489:Addison-Wesley Publishers Ltd.
123:Classical minimization methods
1:
982:Electronic circuit simulators
934:. pp. 136–137, 140–141.
870:"Logic Friday program (2012)"
544:Memorandum No. UCB/ERL M86-65
335:
226:field-programmable gate array
159:-cover or DC-cover) a set of
72:for storing information, and
31:for efficiently reducing the
876:. 2018-09-21. Archived from
312:educational design package.
216:(Programmable Array Logic).
131:by hand using the classical
23:is a computer program using
7:
389:. New York, New York, USA:
240:
235:
10:
998:
455:Kluwer Academic Publishers
295:
693:Contemporary Logic Design
577:10.1109/TCAD.1987.1270318
306:synchronous state machine
269:systems, is available in
977:Free simulation software
972:Electronics optimization
604:University of California
602:(PhD thesis). Berkeley:
249:program is available as
21:ESPRESSO logic minimizer
721:Lala, Parag K. (1996).
654:Design of Logic Systems
650:Lewin, Douglas (1985).
491:pp. 112, 115–116.
441:McMullen, Curtis Tracy
74:combinational circuits
253:source code from the
619:De Micheli, Giovanni
557:Rudell, Richard L.;
517:ark:/13960/t2f83p38r
354:Digital Logic Design
147:. Starting with the
759:Columbia University
350:Hayes, John Patrick
82:combinational logic
688:Borriello, Gaetano
684:Katz, Randy Howard
274:Linux distribution
180:ESPRESSO algorithm
117:logic optimization
109:logic minimization
899:"Espresso-IISOJS"
515:978-0-201-14545-8
129:Boolean functions
98:7-segment display
989:
953:
941:9-783540-56788-2
909:
908:
895:
889:
888:
886:
885:
866:
860:
859:
846:
840:
839:
837:
836:
817:
811:
810:
808:
807:
786:
780:
779:
777:
776:
771:
769:10.7916/D8N58V58
749:
743:
742:
718:
712:
711:
680:
674:
673:
657:
647:
641:
640:
615:
609:
608:(ESPRESSO-EXACT)
607:
595:
589:
588:
554:
548:
547:
546:. Berkeley, USA.
541:
532:
526:
525:
523:
522:
478:
469:
468:
436:
427:
426:
424:
423:
404:
395:
394:
378:
372:
371:
346:
325:unit propagation
161:prime implicants
145:Edward McCluskey
997:
996:
992:
991:
990:
988:
987:
986:
957:
956:
942:
932:Springer-Verlag
918:
916:Further reading
913:
912:
897:
896:
892:
883:
881:
868:
867:
863:
848:
847:
843:
834:
832:
819:
818:
814:
805:
803:
788:
787:
783:
774:
772:
750:
746:
739:
719:
715:
708:
681:
677:
670:
648:
644:
637:
616:
612:
596:
592:
555:
551:
539:
533:
529:
520:
518:
499:
479:
472:
465:
437:
430:
421:
419:
406:
405:
398:
379:
375:
368:
347:
343:
338:
321:ESPRESSO-IISOJS
318:
316:ESPRESSO-IISOJS
298:
282:
243:
238:
221:logic synthesis
182:
125:
105:
90:logic synthesis
70:memory elements
66:
56:in the form of
54:logic functions
50:
17:
12:
11:
5:
995:
985:
984:
979:
974:
969:
955:
954:
940:
917:
914:
911:
910:
890:
861:
841:
827:. 2018-09-21.
812:
798:. 2018-09-21.
781:
744:
737:
713:
706:
675:
668:
642:
635:
610:
590:
571:(5): 727–750.
549:
527:
497:
470:
463:
428:
414:. 2018-09-23.
396:
373:
366:
358:Addison Wesley
340:
339:
337:
334:
317:
314:
297:
294:
281:
278:
242:
239:
237:
234:
198:global minimum
181:
178:
166:Although this
124:
121:
102:
78:State machines
65:
62:
49:
46:
15:
9:
6:
4:
3:
2:
994:
983:
980:
978:
975:
973:
970:
968:
965:
964:
962:
951:
950:3-540-56788-7
947:
943:
937:
933:
929:
925:
920:
919:
906:
905:
900:
894:
880:on 2013-10-22
879:
875:
871:
865:
857:
856:
851:
845:
830:
826:
822:
816:
801:
797:
796:
791:
785:
770:
765:
761:
760:
755:
748:
740:
738:0-02-367171-8
734:
730:
729:Prentice Hall
726:
725:
717:
709:
707:0-8053-2703-7
703:
699:
695:
694:
689:
685:
679:
671:
669:0-442-30606-7
665:
661:
656:
655:
646:
638:
636:0-07-016333-2
632:
628:
624:
620:
614:
605:
601:
594:
586:
582:
578:
574:
570:
566:
565:
560:
553:
545:
538:
531:
516:
512:
508:
504:
500:
498:0-201-14545-6
494:
490:
486:
485:
477:
475:
466:
464:0-89838-164-9
460:
456:
452:
451:
446:
442:
435:
433:
417:
413:
409:
403:
401:
392:
388:
384:
377:
369:
367:0-201-15461-7
363:
359:
355:
351:
345:
341:
333:
331:
326:
322:
313:
311:
307:
302:
293:
290:
286:
277:
275:
272:
268:
264:
260:
256:
252:
248:
245:The original
233:
231:
228:(FPGA) or an
227:
222:
217:
215:
211:
205:
203:
199:
193:
191:
187:
177:
174:
173:exponentially
169:
164:
162:
158:
154:
150:
146:
142:
141:Willard Quine
137:
134:
133:Karnaugh maps
130:
120:
118:
112:
110:
101:
99:
93:
91:
86:
83:
79:
75:
71:
61:
59:
55:
45:
42:
38:
34:
30:
27:and specific
26:
22:
927:
923:
902:
893:
882:. Retrieved
878:the original
873:
864:
853:
844:
833:. Retrieved
824:
815:
804:. Retrieved
793:
784:
773:. Retrieved
757:
747:
723:
716:
692:
678:
660:Van Nostrand
653:
645:
622:
613:
599:
593:
568:
562:
552:
543:
530:
519:. Retrieved
483:
449:
420:. Retrieved
386:
376:
353:
344:
330:Kleene logic
320:
319:
309:
300:
299:
285:Logic Friday
284:
283:
280:Logic Friday
262:
258:
246:
244:
218:
206:
194:
183:
165:
138:
126:
113:
108:
106:
94:
87:
67:
51:
48:Introduction
20:
18:
825:Google Code
332:functions.
259:ESPRESSO-AB
149:truth table
127:Minimizing
35:of digital
961:Categories
884:2018-09-21
835:2018-09-21
806:2018-09-21
775:2021-10-04
762:(Report).
521:2021-04-17
422:2018-09-23
336:References
287:is a free
202:redundancy
157:Don't-Care
58:logic gate
37:logic gate
33:complexity
29:algorithms
25:heuristic
829:Archived
800:Archived
690:(1994).
621:(1994).
585:13525177
507:90000007
447:(1984).
416:Archived
393:: 42–48.
352:(1993).
310:Publicad
247:ESPRESSO
241:ESPRESSO
236:Software
232:(ASIC).
153:minterms
874:sontrak
301:Minilog
296:Minilog
289:Windows
263:EQNTOTT
948:
938:
904:GitHub
855:GitHub
735:
704:
666:
662:(UK).
633:
583:
513:
505:
495:
461:
364:
271:Debian
190:hazard
926:[
581:S2CID
540:(PDF)
267:POSIX
946:ISBN
936:ISBN
733:ISBN
702:ISBN
664:ISBN
631:ISBN
511:ISBN
503:LCCN
493:ISBN
459:ISBN
391:IEEE
362:ISBN
261:and
143:and
19:The
764:doi
573:doi
214:PAL
210:PLA
41:IBM
963::
944:.
901:.
872:.
852:.
823:.
792:.
756:.
731:.
727:.
700:.
696:.
686:;
658:.
629:.
625:.
579:.
567:.
542:.
509:.
501:.
473:^
457:.
443:;
431:^
410:.
399:^
360:.
356:.
119:.
952:.
907:.
887:.
858:.
838:.
809:.
778:.
766::
741:.
710:.
672:.
639:.
606:.
587:.
575::
569:6
524:.
467:.
425:.
370:.
251:C
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.