{"id":726,"date":"2012-10-27T16:18:00","date_gmt":"2012-10-27T08:18:00","guid":{"rendered":"http:\/\/note.systw.net\/note\/?p=726"},"modified":"2023-11-04T16:30:07","modified_gmt":"2023-11-04T08:30:07","slug":"%e7%b5%84%e5%90%88%e9%9b%bb%e8%b7%af","status":"publish","type":"post","link":"https:\/\/systw.net\/note\/archives\/726","title":{"rendered":"\u7d44\u5408\u96fb\u8def"},"content":{"rendered":"\n

\u5e03\u6797\u4ee3\u6578<\/strong><\/p>\n\n\n\n

\u5e03\u6797\u4ee3\u6578\u5b9a\u7406<\/strong><\/td>AND<\/strong><\/td>OR<\/strong><\/td><\/tr>
identify law<\/td>1*A=A<\/td>0+A=A<\/td><\/tr>
null law<\/td>0*A=0<\/td>1+A=1<\/td><\/tr>
idem law<\/td>A*A=A<\/td>A+A=A<\/td><\/tr>
inverse law<\/td>A*A’=0<\/td>A+A’=1<\/td><\/tr>
commutative law<\/td>A*B=B*A<\/td>A+B=B+A<\/td><\/tr>
associative law<\/td>(A*B)*C=A*(B*C)<\/td>(A+B)+C=A+(B+C)<\/td><\/tr>
distributive law<\/td>A+B*C=(A+B)*(A+C)<\/td>A*(B+C)=A*B+A*C<\/td><\/tr>
absorption law<\/td>A*(A+B)=A<\/td>A+A*B=A<\/td><\/tr>
demorgan’s law<\/td>(A*B)’=A’+B’<\/td>(A+B)’=A’*B’<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n

n \u500b\u8f38\u5165\u8b8a\u6578,\u67092^n\u500b\u4e0d\u540c\u7684\u8f38\u5165\u8b8a\u6578\u7d44\u5408,\u5247:
minterm(\u6700\u5c0f\u9805),standard product(\u6a19\u6e96\u4e58\u7a4d\u9805):\u5c07n\u500b\u8f38\u5165\u8b8a\u6578\u7528and\u904b\u7b97\u7d50\u5408,\u82e5\u8f38\u5165\u8b8a\u6578\u7684\u503c\u70ba0,\u5247\u8b8a\u6578\u52a0\u4e0a\u53cd\u76f8\u7b26\u865f
maxterm(\u6700\u5927\u9805),standard sum(\u6a19\u6e96\u548c\u9805):\u5c07n\u500b\u8f38\u5165\u8b8a\u6578\u7528or\u904b\u7b97\u7d50\u5408,\u82e5\u8f38\u5165\u8b8a\u6578\u7684\u503c\u70ba1,\u5247\u8b8a\u6578\u52a0\u4e0a\u53cd\u76f8\u7b26\u865f
\u4e14(minterms)’=maxterms<\/p>\n\n\n\n

\u6700\u5c0f\u9805\u8868\u793a\u6cd5<\/strong>,\u4e5f\u7a31SOP(sum-of-minterms,sum-of-products,\u6700\u5c0f\u9805\u4e4b\u548c),\u7a4d\u4e4b\u548c\u578b\u5f0f
\u3000\u5c07\u6240\u6709\u8f38\u51fa\u70ba1\u7684\u6700\u5c0f\u9805\u7528 or\u9023\u63a5
\u6700\u5927\u9805\u8868\u793a\u6cd5<\/strong>,\u4e5f\u7a31POS(product-of-minterms,product-of-sums,\u6700\u5927\u9805\u4e4b\u7a4d),\u548c\u4e4b\u7a4d\u578b\u5f0f
\u3000\u5c07\u6240\u6709\u8f38\u51fa\u70ba0\u7684\u6700\u5c0f\u9805\u7528and\u9023\u63a5<\/p>\n\n\n\n

ex:\u8a2df(a,b,c)\u7684minterms,maxterms,\u5047\u8a2d\u8f38\u51fa\u7d50\u679c\u5982\u4e0b<\/p>\n\n\n\n

f(a,b,c)<\/td>minterms<\/td>maxterms<\/td>\u5047\u8a2d\u8f38\u51fa\u7d50\u679c<\/td>(minterms)’=maxterms<\/td><\/tr>
0 0 0<\/td>a’*b’*c’<\/td>a+b+c<\/td>0<\/td>(a’*b’*c’)’=a+b+c<\/td><\/tr>
0 0 1<\/td>a’*b’*c<\/td>a+b+c’<\/td>0<\/td>(a’*b’*c)’=a+b+c’<\/td><\/tr>
0 1 0<\/td>a’*b*c’<\/td>a+b’+c<\/td>0<\/td>(a’*b*c’)’=a+b’+c<\/td><\/tr>
0 1 1<\/td>a’*b*c<\/td>a+b’+c’<\/td>1<\/td>(a’*b*c)’=a+b’+c’<\/td><\/tr>
1 0 0<\/td>a*b’*c’<\/td>a’+b+c<\/td>0<\/td>(a*b’*c’)’=a’+b+c<\/td><\/tr>
1 0 1<\/td>a*b’*c<\/td>a’+b+c’<\/td>1<\/td>(a*b’*c)’=a’+b+c’<\/td><\/tr>
1 1 0<\/td>a*b*c’<\/td>a’+b’+c<\/td>1<\/td>(a*b*c’)’=a’+b’+c<\/td><\/tr>
1 1 1<\/td>a*b*c<\/td>a’+b’+c’<\/td>1<\/td>(a*b*c)’=a’+b’+c’<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n

\u6700\u5c0f\u9805\u8868\u793a\u6cd5 f(a,b,c)=m3+m5+m6+m7=a’*b*c+a*b’*c+a*b*c’+a*b*c
\u6700\u5927\u9805\u8868\u793a\u6cd5 f(a,b,c)=M0*M1*M2*M4=(a+b+c)*(a+b+c’)*(a+b’+c)*(a’+b’+c)<\/p>\n\n\n\n

………….<\/p>\n\n\n\n

\u908f\u8f2f\u9598<\/strong>
nor,nand,or,and,not \u70ba\u57fa\u672c\u908f\u8f2f\u9598
nor,nand\u96fb\u8def\u6bd4or,and\u96fb\u8def\u7c21\u55ae
xor\u908f\u8f2f\u9598\u70ba\u5947\u6578\u51fd\u6578,\u82e52\u500b\u8f38\u5165\u8b8a\u6578\u4e0d\u540c\u5247\u8f38\u51fa\u70ba1
xnor\u908f\u8f2f\u9598\u70ba\u5076\u6578\u51fd\u6578,\u82e52\u500b\u8f38\u5165\u8b8a\u6578\u76f8\u540c\u5247\u8f38\u51fa\u70ba1<\/p>\n\n\n\n

\u8f38\u5165<\/td>and<\/td>nand<\/td>or<\/td>nor<\/td>xor<\/td>xnor<\/td><\/tr>
0 0<\/td>0<\/td>1<\/td>0<\/td>1<\/td>0<\/td>1<\/td><\/tr>
0 1<\/td>0<\/td>1<\/td>1<\/td>0<\/td>1<\/td>0<\/td><\/tr>
1 0<\/td>0<\/td>1<\/td>1<\/td>0<\/td>1<\/td>0<\/td><\/tr>
1 1<\/td>1<\/td>0<\/td>1<\/td>0<\/td>0<\/td>1<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n

complete set of operators(\u904b\u7b97\u5b50\u5b8c\u5168\u96c6)<\/strong>
\u53ef\u4ee5\u7d44\u5408\u51fa\u6240\u6709\u7d44\u5408\u96fb\u8def\u7684\u4e00\u7d44\u5e03\u6797\u904b\u7b97\u5b50
3\u500b\u7d44\u5408\u7684\u6709{and,or,not}
2 \u500b\u7d44\u5408\u7684\u6709{and,not},{or,not},{and,xor},{or,xor}
1\u500b\u7d44\u5408\u7684\u6709{nand},{nor}, {minority}<\/p>\n\n\n\n

nor\u901a\u7528\u9598\u53ef\u88fd\u4f5c\u4ee5\u4e0b\u908f\u8f2f\u9598<\/strong>
not\u908f\u8f2f\u9598:(a+a)’=a’,\u9700\u89811\u500bnor\u901a\u7528\u9598
or\u908f\u8f2f\u9598:((a+b)’+(a+b)’)’=((a+b)’)’=a+b,\u9700\u89812\u500bnor\u901a\u7528\u9598
and \u908f\u8f2f\u9598:((a+a)’+(b+b)’)’=(a’+b’)’=a*b,\u9700\u89813\u500bnor\u901a\u7528\u9598
\u9069\u5408\u6700\u5927\u9805\u8868\u793a\u6cd5\u88fd\u4f5c<\/p>\n\n\n\n

nand\u901a\u7528\u9598\u53ef\u88fd\u4f5c\u4ee5\u4e0b\u908f\u8f2f\u9598<\/strong>
not\u908f\u8f2f\u9598:(a*a)’=a’,\u9700\u89811\u500bnor\u901a\u7528\u9598
or\u908f\u8f2f\u9598:((a*a)'(b*b)’)’= (a’*b’)’=a+b,\u9700\u89813\u500bnor\u901a\u7528\u9598
and\u908f\u8f2f\u9598:((a*b)'(a*b)’)’=((a*b)’)’=a*b,\u9700\u89812\u500bnor\u901a\u7528\u9598
\u9069\u5408\u6700\u5c0f\u9805\u8868\u793a\u6cd5\u88fd\u4f5c<\/p>\n\n\n\n

minority\u901a\u7528\u9598\u53ef\u88fd\u4f5c\u4ee5\u4e0b\u908f\u8f2f<\/strong>
not\u908f\u8f2f\u9598:minority(a,a,a)=a’
or \u908f\u8f2f\u9598:minority(a,b,1)=a+b
and\u908f\u8f2f\u9598:minority(a,b,0)=a*b<\/p>\n\n\n\n

……………..<\/p>\n\n\n\n

\u5e03\u6797\u4ee3\u6578\u5316\u7c21<\/strong>
\u5e38\u898b\u65b9\u6cd5\u6709\u4ee5\u4e0b\uff1a
\u516c\u5f0f\u5316\u7c21\u6cd5<\/strong>
\u3000\u4f7f\u7528\u5e03\u6797\u4ee3\u6578\u5b9a\u7406\u5c0d\u5e03\u6797\u51fd\u6578\u9032\u884c\u5316\u7c21
\u3000\u9069\u7528\u5e03\u6797\u51fd\u6578\u7684\u6700\u5c0f\u9805\u5f88\u5c11\u6642,\u4e14\u8f38\u5165\u8b8a\u6578\u591a\u6642
\u5361\u8afe\u5716\u5316\u7c21\u6cd5<\/strong>
\u3000\u4f7f\u7528\u5361\u8afe\u5716,\u7121\u56fa\u5b9a\u7a0b\u5e8f
\u3000\u9069\u7528\u8f38\u5165\u8b8a\u6578\u5c0f\u65bc6
\u8868\u683c\u5316\u7c21\u6cd5<\/strong>
\u3000\u7531\u5361\u8afe\u5716\u5316\u7c21\u5316\u6539\u826f\u800c\u6210
\u3000\u9069\u7528\u8981\u5316\u7c21\u591a\u500b\u5e03\u6797\u51fd\u6578,\u4e14\u8f38\u5165\u8b8a\u6578\u5f88\u591a\u6642<\/p>\n\n\n\n

\u5361\u8afe\u57162\u500b\u8b8a\u6578
 b’ba’  a 
<\/td>
\u5361\u8afe\u57163\u500b\u8b8a\u6578
 c’ca’b’  a’b  ab  ab’ <\/td>
\u5361\u8afe\u57164\u500b\u8b8a\u6578
 c’d’c’dcdcd’a’b’    a’b    ab    ab’   <\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n

………………<\/p>\n\n\n\n

\u7d44\u5408\u96fb\u8def\u8a2d\u8a08\u7a0b\u5e8f<\/strong>
1\u771f\u503c\u8868
2\u6a19\u6e96\u7684\u6700\u5c0f\u9805\u4e4b\u548c\u8868\u793a\u5f0f
3\u6a19\u6e96\u7684\u5e03\u6797\u51fd\u6578\u5316\u7c21
4\u756b\u51fa\u5c0d\u61c9\u7684\u7d44\u5408\u96fb\u8def
\u5e38\u898b\u7684\u7d44\u5408\u96fb\u8def\u6709: \u534a\u52a0\u5668,\u5168\u52a0\u5668,n\u4f4d\u5143\u52a0\u6cd5\u5668,bcd\u52a0\u6cd5\u5668
\u5e38\u898b\u8f03\u8907\u96dc\u7684\u7d44\u5408\u96fb\u8def\u6709:decoder,multiplexer,rom,PLA,…\u7b49<\/p>\n\n\n\n

half ader(\u534a\u52a0\u5668)<\/strong>
2\u500b\u8f38\u5165\u8b8a\u6578:x(\u88ab\u52a0\u6578),y(\u52a0\u6578)
2\u500b\u8f38\u51fa\u8b8a\u6578:carry(\u9032\u4f4d),sum(\u548c)
\u771f\u503c\u8868\u5982\u4e0b<\/p>\n\n\n\n

x y<\/td>carry<\/td>sum<\/td><\/tr>
0 0<\/td>0<\/td>0<\/td><\/tr>
0 1<\/td>0<\/td>1<\/td><\/tr>
1 0<\/td>0<\/td>1<\/td><\/tr>
1 1<\/td>1<\/td>0<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n

carry(x,y)=m3=xy
sum(x,y)=m1+m2=x’y+xy’<\/p>\n\n\n\n

full adder(\u5168\u52a0\u5668)<\/strong>
3 \u500b\u8f38\u5165\u8b8a\u6578:x(\u88ab\u52a0\u6578),y(\u52a0\u6578),c(\u9032\u4f4d)
2\u500b\u8f38\u51fa\u8b8a\u6578:carry(\u9032\u4f4d),sum(\u548c)
\u771f\u503c\u8868\u5982\u4e0b<\/p>\n\n\n\n

x y c<\/td>carry<\/td>sum<\/td><\/tr>
0 0 0<\/td>0<\/td>0<\/td><\/tr>
0 0 1<\/td>0<\/td>1<\/td><\/tr>
0 1 0<\/td>0<\/td>1<\/td><\/tr>
0 1 1<\/td>1<\/td>0<\/td><\/tr>
1 0 0<\/td>0<\/td>1<\/td><\/tr>
1 0 1<\/td>1<\/td>0<\/td><\/tr>
1 1 0<\/td>1<\/td>0<\/td><\/tr>
1 1 1<\/td>1<\/td>1<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n

carry(x,y,c)=m3+m5+m6+m7=x’yc+xy’c+xyc’+xyc
sum(x,y,c)=m1+m2+m4+m7=x’y’c+x’yc’+xy’c’+xyc<\/p>\n\n\n\n

decoder(\u89e3\u78bc\u5668)<\/strong>
\u5c07n\u500b\u8f38\u5165\u7dda\u89e3\u78bc\u6210\u6700\u591a2^n\u500b\u8f38\u51fa\u7dda,\u4e5f\u5c31\u662fn-to-m decoder
encoder(\u7de8\u78bc\u5668)<\/strong>
\u5c072^n\u500b\u8f38\u5165\u7dda\u7de8\u78bc\u6210n\u500b\u8f38\u51fa\u7dda<\/p>\n\n\n\n

multiplexer(\u591a\u5de5\u5668)<\/strong>
\u4e5f\u7a31\u70badata selector(\u8cc7\u6599\u9078\u64c7\u5668)
\u4f7f\u7528\u5c11\u6578\u7684\u8f38\u51fa\u7dda\u540c\u6642\u50b3\u9001\u591a\u500b\u8f38\u5165\u7dda\u7684\u5927\u91cf\u8cc7\u6599,\u5229\u7528\u4e00\u7d44\u9078\u64c7\u7dda\u4f86\u9078\u53d6\u5176\u4e2d\u4e00\u689d\u8f38\u5165\u7dda\u9032\u884c\u50b3\u9001
\u82e5\u67092^n\u689d\u8f38\u5165\u7dda,\u5247\u9700\u4f7f\u7528n\u689d\u9078\u64c7\u7dda
ps:
\u4f7f\u75283\u500b4to1 multiplexer=1\u500b8to1 multiplexer
\u4f7f\u75287\u500b2to1 multiplexer=1\u500b8to1 multiplexer<\/p>\n\n\n\n

demultiplexer(\u89e3\u591a\u5de5\u5668)<\/strong>
\u4f7f\u75281 \u500b2\u9032\u4f4ddecoder\u548c\u4e00\u689denable\u8f38\u5165\u7dda
\u662f\u7531\u4e00\u689d\u7dda\u8f38\u5165\u7dda\u4e0a\u6536\u5230\u8a0a\u865f,\u518d\u5206\u5225\u50b3\u52302^n\u500b\u4e0d\u540c\u8f38\u51fa\u7dda\u7684\u5176\u4e2d\u4e00\u689d,\u4f7f\u7528n\u500b\u9078\u64c7\u7dda\u505a\u63a7\u5236<\/p>\n\n\n\n

comparator(\u6bd4\u8f03\u5668)<\/strong>
\u7528\u4f86\u6bd4\u8f032\u500b\u7121\u865f\u6574\u6578\u7684\u5927\u5c0f\u95dc\u4fc2<\/p>\n\n\n\n

shifter(\u79fb\u4f4d\u5668)<\/strong>
\u53ef\u5c07\u8cc7\u6599\u5f80\u5de6\u6216\u662f\u5f80\u53f3\u79fb\u52d5\u4e00\u500b\u4f4d\u5143<\/p>\n\n\n\n

Flip-Flop(\u6b63\u53cd\u5668)<\/strong>
\u53ef\u4ee5\u5132\u5b58\u4e00\u500b\u4f4d\u5143\u7684\u96fb\u8def
\u662f\u8a08\u6578\u5668,\u66ab\u5b58\u5668,\u5176\u4ed6\u6642\u5e8f\u63a7\u5236\u908f\u8f2f\u96fb\u8def\u4e2d\u7684\u4e00\u500b\u57fa\u672c\u5efa\u69cb\u65b9\u584a<\/p>\n","protected":false},"excerpt":{"rendered":"

\u5e03\u6797\u4ee3\u6578 \u5e03\u6797\u4ee3\u6578\u5b9a\u7406 AND OR identify la …<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"fifu_image_url":"","fifu_image_alt":"","_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":false,"jetpack_social_options":{"image_generator_settings":{"template":"highway","default_image_id":0,"font":"","enabled":false},"version":2}},"categories":[23],"tags":[],"class_list":["post-726","post","type-post","status-publish","format-standard","hentry","category-computerarchitecture"],"jetpack_publicize_connections":[],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/systw.net\/note\/wp-json\/wp\/v2\/posts\/726","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/systw.net\/note\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/systw.net\/note\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/systw.net\/note\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/systw.net\/note\/wp-json\/wp\/v2\/comments?post=726"}],"version-history":[{"count":0,"href":"https:\/\/systw.net\/note\/wp-json\/wp\/v2\/posts\/726\/revisions"}],"wp:attachment":[{"href":"https:\/\/systw.net\/note\/wp-json\/wp\/v2\/media?parent=726"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/systw.net\/note\/wp-json\/wp\/v2\/categories?post=726"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/systw.net\/note\/wp-json\/wp\/v2\/tags?post=726"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}