数字电路基础与入门

1-11-21.11.21.31.41.51-31.11.1.11-4tV(t)tV(t)1-51.2.1-6::••••(••…1-7•••••A/DD/A1-81.1.21234567890157=012107105101×+×+×N∑∞-∞=×=iiiDKN10)(1-901∑∞-∞=×=iiiBKN21001B=012321202021×+×+×+×=(9)D---1-100123456789A(10)B(11)C(12)D(13)E(14)F(15)(4E6)H=4×162+14×161+6×160=(1254)D(F)H(1111)B1.HexadecimalDecimalBinary1-11(01011001)B=[0×27+1×26+0×25+1×24+1×23+0×22+0×21+1×20]D=[(0×23+1×22+0×21+1×20)×161+(1×23+0×22+0×21+1×20)×160]D=(59)H216(10011100101101001000)B=(10011100101101001000)B()H84BC9=(9CB48)H1-122.(10011100101101001000)O=(10011100101101001000)B()O01554=(2345510)O3201234567(7)O(111)B1-13∑∞=×=02iiiDKN222011KKNiiiD+×=∑∞=-2221222KKNiiiD+×=∑∞=-20K021K10K01K12K2…………1-14225……1……K0122……0……K162……0……K232……1……K312……1……K4025(25)D=(11001)B1-151.1.3NNn≥2–BCD-Binary-Coded-Decimal1-16BCD0~916160~98421542132421(3256)D=3×103+2×102+5×101+6×100(D0)100(D1)101(D2)102(D3)103……1-17(N)D(K3K2K1K0)B(N)D=W3K3+W2K2+W1K1+W0K0W3~W08421W3=8W3=4W3=2W3=10~92421W3=2W3=4W3=2W3=15421W3=5W3=4W3=2W3=11-180000000100100011011001111000100110101011110111101111010111000100012367891011131415512401235789640123567894034567829101236785498421242154211-19(and)(or)(not)1.2:“1”“0”“1”“0”EFABC1-20&ABCFAFBC00001000010011000010101001101111F=A•B•CEFABC:00,110•0=00•1=01•0=01•1=11-21“”AEFBC:“1”“0”“1”“0”1-22AFBC00001001010111010011101101111111≥1ABCFF=A+B+CAEFBC11,00:0+0=00+1=11+0=11+1=11-23“””:“1”“0”“1”“0”AEFR1-24AF0110AEFR:10,01AF=10,01==AF11-25CBAF⋅⋅=ABCF&ABCF1-26CBAF++=ABCF≥1ABCFBABABAF⊕=+=ABF=1ABCFABF=1ABCFBABAABF⋅=+=1-27&ABYABY11YAY=ABY=A+B&ABYABY1=1ABYY=A⊕BAY=ABY=BAY+=1-281.30101011-291.3.1:0+0=00+1=11+0=11+1=1:0•0=00•1=01•0=01•1=1:1001==AA=0,,1,00=⋅=⋅=⋅=⋅AAAAAAAA1,,11,0=+=+=+=+AAAAAAAA1-301.3.2A+B=B+AA•B=B•AA+(B+C)=(A+B)+C=(A+C)+BA•(B•C)=(A•B)•CA(B+C)=A•B+A•CA+B•C=(A+B)(A+C)!1-31:2A+BC=(A+B)(A+C):=(A+B)(A+C)=AA+AB+AC+BC;=A+A(B+C)+BC;,AA=A=A(1+B+C)+BC;=A•1+BC;1+B+C=1=A+BC;A•1=1=1-321.A+AB=AA+AB=A(1+B)=A•1=ACDAB)FE(DABCDAB+=+++⇒1-332.BABAA+=+BAABABAA++=+BA)AA(BA+=++=DEBCADCBCAA++=++1-343.CAABBCCAAB+=++BC)AA(CAABBCCAAB+++=++CAABBCAABCCAAB+=+++=CAABBCCAABBCDBCCAABBCDCAAB+=++=+++=++11-35BABABABA⋅=++=⋅ABA•B0001111010110110010111110000BA•ABBA+•(De•Morgan)1-36F•++•1.⇒⇒2.:F'FF=′()1-3711)()(1⋅+⋅+=DCBAF01+⋅+⋅=DCBAF─01+⋅+⋅=DCBAFDBDACBCAF+++=1∴1-38)(EDCBA+++⋅=)(EDCBA⋅++⋅=2EDCBAF2++++=EDCBAF⋅⋅⋅⋅=2─EDCBAF++++=2EDACABAF⋅⋅+⋅+⋅=2∴1-391.4(,)11&&1ABY:n2nBABAF+=1-40n2nABCF000000100100011010001011110111111.4.11-411.4.2ABCCBACBACBACBAF++++=——1-42ABCF00000010010001101000101111011111CBACBACBABCACBACBACABABC101-43(1)ABCF00000010010001101000101111011111CBACBACBABCACBACBACABABC(2)101-44ABCF00000010010001101000101111011111CBACBACBABCACBACBACABABC33CBACBACABCBAABCCCBBAA+++=++=))((1-45ABCF00000010010001101000101111011111CBACBACBABCACBACBACABABCABCCABCBAF++=1-46BCACBAABCF00000010010001101000101111011111CBACBACBABCACBACBACABABCCBACBA1-47ABCCBACBACBACBAF++++=CBCBACBA=+1-481.4.3nn1-49ABY001011101110AB01010111Y11-500100011110ABC00000111YABCY00000010010001101000101111011111200101-51ABCD00011110000111011010111111100010DCBAABCD=01000131-52ABC00011110010132456F(A,B,C)=Σ(1,2,4,7)1,2,4,710ABC000000110102011310041015110611171-53013245612148910ABCD0001111000011110:1-541.4.4&AB&CD≥1FF=AB+CD1-551.4.5↔BABY=AB+ABABA1&AB&111-56↔ABY001011101110AB101011101-57↔1“”ABY001011101110AB01010111ABY=ABABABBABABAY++=1-581.51.5.11ABAC)BC(A)BCB(AABCBA)CC(ABCBAABCCABCBAF+=+=+=+=++=++=AB=1A1-592CBBCBAABF+⋅+=)(CBBCBAAB+++=CBAABCCCBAAB+++++=)()(CBBCAABCCBACBAAB+++++=CBBBCAAB+++=)(CBCAAB++=1-6043:BABBAABABABAY⋅⋅⋅⋅⋅=+=⊕=BABBAA⋅⋅+⋅⋅=;AB=A+BBABBAA⋅⋅+⋅⋅=)BA(B)BA(A+⋅++⋅=BBABBAAA⋅+⋅+⋅+⋅=0ABBA0+⋅+⋅+=ABBA⋅+⋅==AA;=;BABA;⋅=+1-614&&&&ABYBABBAABABABAY⋅⋅⋅⋅⋅=+=⊕=1-624ABCCABCBABCACBAY++++=ABCCABCBABCACBAY++++=)CC(ABCBA)CC(BA++++=ABCBABA++=CBAB)AA(++=CBAB+=ACB+=1-635Y;;A+AB=A+BA=ACDBABAY)(++=CD)BA(BAY++=CDBABA)(++=CDBABA+=CDBA+=1-641.5.2ABC00011110010010001ABCBCABCBCAABC=+AB=1C=1“1”1-65ABC00011110010010001ABBCF=AB+BC341-661.2nABCD0001111000010000000001101110ADAB000001010100CD00011110000111101-674.“”“”“”2.2nn3.15.121222...1-681F(A,B,C,D)=Σ(0,2,3,5,6,8,9,10,11,12,13,14,15)ABCD0001111000011011011111111110ADCCBDBDCBDCBDBCBDCAF++++=1-692ABCD00011110000111111111100111111110ABDABDF=1-703→CAB0100011110ABCBACBAABY++=CBABY+=CB1-714ABCF00000010010001101001110111111011-72ABC0001111001000011101AF=A1-73ABC0100011110111111ABC0100011110111111CBCABAY++=CABACBY++=1-74CBCABAY++=“”“”CBCABACBCABACBCABAY⋅⋅=++=++=1-75