数字电路与逻辑设计课后习题测验答案蔡良伟第三版

1、数字电路答案数字电路答案第一章习题1- 1(1) 2210 = 2*8 1 + 6*8 0 = 268268 = 2 6 = 1011Q010110101102 = 00010110= 1%1 62 10(2) 10810 = 1*8 + 5*8 + 4*8 = 15481548 = 1 5 4 = 110110Q001101100110110C2 = 01101100= 6C166 C1 0 - 1(3) 13.12510 = 1*8 1 + 5*8 0 + 1*8 1 = 15.1815.18 = 1 5. 1 = 1101.0012001101 0011101.00! = 1101.00

2、10= D26D22 10 1(4) 131.62510 = 2*8 + 0*8 + 3*8 + 5*8 - = 203.58203.58 = 2 0 3. 5 = 10000011.101010 000 011 10110000011.10!= 10000011.1010= 83.A1683A1-2(1)1011012 =101101= 558551011012 =00101101= 2D162D558 = 5*8'+ 5*8 0 = 4510(2)11100101=011100101= 34583451110010! = 11100101= E516E 53458 = 3*8 2

3、+ 4*8 1 + 5*8 0 = 229®(3) 101.0011= 101.001100= 5.148514101.001!= 0101.0011= 5.36535. 14=5*H81 *+8- 4=* 85o 1 87 5(4) 100111.101 = 100111.101= 47.4474100111.101 = 00100111.1010= 27A1627A1 0 147.54* 8 0528= 5*8 + 2*8 = 42107*805*8-39.625101- 3(1) 168 = 1*8 1 + 6*8 0 = 1410168= 1 6 = 111020011101

4、110=11=低16E2 10(2) 1728 = 1*8 2 + 7*8 1 + 2*8 ° = 122101728 = 1 7 2 = 11110102001111 01011110102 二 01111010 二 7A167 A1 0 - 1 - 2(3) 61.538 = 6*8 + 1*8 + 5*8+ 3*8= 49.6721。61.538 = 6 1.5 3 = 110001.101011110001 101 011110001.101011 = 00110001.10101100= 31.AC163 1A C21012(4) 126.748 = 1*8 + 2*8 +

5、 6*8 + 7*8 - + 4*8 - = 86.937510126.74 = 1 2 6. 7 4 = 1010110.1111001 010110 1111001010110.1111= 01010110.1111= 56.F1656F1- 4(1) 2人6= 2 A = 1010102001010101010102 = 101010= 52852(2) B2F16 = B 2 F = 1011001011111011 00101111101100101111= 101100101111= 54578545754578 = 5*8 3 + 4*8 2 + 5*8 1 + 7*8 0 =

6、286310(3) D3.E16= D 3 . E = 11010011.1111101 0011 111011010011.111= 011010011.111= 323.783 2372 10 1323.78 = 3*8 + 2*8 + 3*8 + 7*8 - = 211.87510(4) 1C3.F916= 1 C 3 . F 9 = 111000011.1111100100011100 0011 11111001111000011.11111001= 111000011.111110010= 703.7628703762210. 1. 2 3703.7628= 7*8 + 0*8 +

7、3*8 + 7*8+ 6*8+ 2*8= 451.97261。1- 5(1) A(B C)二 AB ACABC左式右式0000000100010000110010000101111101111111左式=右式，得证。(2) A BC -(A B)(A C)ABCr左式右式0000000100010000111110011101111101111111左式=右式，得证。35(3) A B =ABAB左式右式0011010010001100左式=右式，得证。(4) AB = A BAB左式右式0011011110111100左式=右式，得证。(5) A BC ABC =1ABCr左式右式00011

8、00111010110111110011101111101111111左式=右式，得证。(6)ab Ab 二 ab ABAB左式右式0000011110111100左式=右式，得证。(7) A 二 B = A 二 BAB左式右式0000011110111100左式=右式，得证。(8) AB 亠 BC 亠CA = AB 亠 BC 亠CAABC左式右式0000000111010110111110011101111101111100左式=右式，得证。1- 6(1) A+ AB+ B = 1证：A+ AB+ B = A+ B + B = A+ 1= 1(2) A+ BA+ CD = A证：A BA C

9、D 二 A ACD 二 A aCD 二 A(1 CD) = A(3) AB+ AC+ BC= AB+ C证：AB+ AC+ BC = AB+ (A+ B)C = AB + ABC = AB+ C(4) AB+ A+ C+ B(D+ E)C = AB+ AC证：AB+ A+ C+ B(D+ E)C= AB+ 7c + BC(D+ E) = AB + AC(5) A? B AB= A+ B证：A? B AB= AB+ Ab+ AB= A+ AB= A+ B(6) AB + BC + C A = ABC + ABC证：AB+ BC + CA = (A+ B)(B + C)(C + A) = ABC

10、+ ABC(7) ABD + BCD + AD+ ABC + ABCD = AB+ AD+ BC证：原式= ABD ABCD BCD AD ABC ABCD (再加一次最后一项)=BD (A+ AC) + BCD + Ad+ BC(A+ AD)=BD(A+ C)+ BCD + AD+ BCAD=BD(A+ C) + B(C + CD )+ AD=ABD + B(CD + C+ D)+ AD=B(AD + D)+ CB+ AD=(AB+ BD+ AD) + CB=AB + AD + BC(8) A 二 B B 二 C C 二 D = AB BC CD DA证：原式=AB Ab BC BC CD

11、CD=ABBCCDABBC CDADDA=ABBCCDDAAb BCCDAD=AB BC CD DA AB BC CD DA=AB BC CD DA1- 7(1) Fi = ABC+ ABC= A B C (A B C)(2) F2 = A(B+ C)+ C(B+ D)爲 h【A BC (C BD)(3) F3 = (A+ B)(C+ D)= AB CD(4) F4 = (AB+ CD)(B+ AD)F4 二 A BC D BAD(5) F5 = AB+ ACB + DF5 = A B A C BD(6) F6 = A+ BC + B + CD尸6 二 A B c bC D(7) F7 = A

12、C+ BDC + A+ BDF7 = A C B D CAB D(8) F8 = (A+ D)(B+ C)+ (A+ C+ B)AB+ CDFg = Ad bCACB A B C d1- 8(1) R = AB + CDFi'= (A+ B)(C+ D)(2) F2 = (A+ B)(C+ D)F2' = AB+ Cd(3) F3= A(B+ D)+ B(A+ C)F3= (A+ BD)(B+ aC)(4) F4 = (A+ BCD)(ABC+ D)F4'= A(B+ C+ D) + (A+ B+ C)D(5) F5 = A+ B+ C+ DF5= ABCD(6) F6

13、 = BC + CDB (AD+ C)F6= (B+ C)(C+ D)+ B+ (A+ D)C(7) F7 = BC + ADAC + C+ ABF7= (B+ C)(A+ D)+ A+ CC A+ B(8) F8 = ABC + A+ CD (BD + C)+ (BC+ A+ D)B+ A+ BCF8'= (A+ B+ C)A(C+ D)+ (B+ D)C(B+ C)AD + BA(B+ C)1-9(i)已=aBc+Abc+ABC + abcA BCF0 0 010 0 100 1 000 1 111 0 001 0 111 1 001 1 110001111010100110(2)

14、 F2 = a+ bc+ cdABCFDABCFD000(P100100000110011001001011000111101110100011010010011101101110111100111111111CD00000111100111100010001111111111(3) F3 = AB+ B(C+ AD)ABCDFABCDF00000100000001010011、CD0001001ABC 0001111011100001100111101110100111000011111010111101011000001101111001001110111111110(4) F4 = (A

15、+ B+ C)(A+ B+ C)(A+ B+ C)BC00 01 11 1011100011(5) F5 = (BD+ C)(C+ AD)ABCDABCD000010000000100100101011000111011010011000100110001101111001111111CD00 01 11 10000111100011001100110111(6) F6 = (AB+CD)(BC+ DA)(AC+ BD)ABCDABCD0000100000001000001010100010101001001100010011000110111001101110CD 00 01 11 1000

16、0111100000000000000000(7) F7 = A+ BC+ BA + C + DABCF 1)ABCFD0001(100100001 1100110010 (101100010 1101110100 (110100100 1110110110 (111100111 111111(8) F8 二 AbD BC CAD D AC BDABCDFABCDFd C 00110 0 010 0 0 11I D 0110 0 101L 01010 0 11110 1110 1 0 01L 10010 10 11110 110 1101111000 1110111101-10标准与或式:11

17、0000101111111111100001111001CD0000co11111011100111011110011110F =ABCD ABCD ABCD ABCD ABCD ABCD ABCD标准或与式:F = A B C D A B C D A B C D A B C d A B C D ABCD A B C D ABCD ABCD1- 11(1) Fi 八 0,2,4,567(2) F2 八 0,2,3,4,5,12,13,15(3) F3 二 '、0,1,2,4,5(4) F4 八 2,4,5,6,7,14,15(5) F5 八 0,3,4,5,6(6) F6 = 10,1

18、,3,4,5,8,10,11,12,13,14,15(7) F7 八 0,2,5,6(8) F81,4,5,7,11,141- 12(1) Fil ：'：.0,7(2) Fil -2,3,5,6,7,13,15(3) F3 F '6,7,11,14,15(4) Fil -0,1,2,3,4,6,7,10,12,14(5) Fil '3,4,5,7(6) F6 八 0,1,5,8,9,10,11,13(7) F7 -IU ：23,5,7(8) F8 Fl10,2,4,7,9,12,151- 13 F =1,3,6,10,11,12F TU 10,2,4,5,7,8,9,1

19、3,14,15(b) F 八 0,3,4,6,8,9,13,15F 訓| ；1,2,5,7,10,11,12,141-14(1) A+ AB+ BCD = A+ B+ BCD = A+ B(2) AB+ BC + A+ C = A+ B+ C + B= 1(3) A+ B+ AB(C+ D)= AB+ AB(C + D) = A+ BAB+ AC + BC + A? B=AB + AC + BC + AB + AB=AB+ AB+ (AC+ AB)+ BC=A+ A+ BC = 1BD+ ABCD + A+ B+ C=BD+ ABCD + ABC=BD+ AC(D+ B)=BD+ ACAB+

20、(A+ C)(D + A+ B)+ (C + D)E(6) = AB + AD + CD + ABC + CDE=AB+ AD + CD+ BC+ EC+ ABCD + CD + (A+ B)(CD + CD )(7) = C+ AB(CD + CD ) + AB(CD + CD )=C + CD + CD = C + D(8) AB + BC + C A + AB = AB + BC + C A+ A + B = A + C + B + C = 11-15(1) AB+ BC+ ACAB+ BC+ AC= A+ BC(2) ABC+ BC+ AD+ CD11100Z|Xy01100uK0VX

21、0001111001CD00ABC+ BC+ AD+ CD = BC+ AC+ D(3) Abc+ abCd+ ABCD+ ACh00R00w00000001111001 11 100000J匚clLx00ABC+ ABCD+ ABCD+ AC = AB+ AC + BCD + BCD(4) B(C+ AD)+ AC(B+ D)CDAB 、0001111000011110B(C+ AD) + AC(B+ D)= AB+ AC+ BD(5) B(C? D) ACD + BCD + BCDAB000八000110h00y0V0000011110011110B(C ? D) ACD + BCD +

22、BCD = CD + BCD(6) ABC + BCD + AD+ A(B + CD)ABC+ BCD + AD+ A(B+ CD)= ABD + ABD + AC(7) ABC + CD + AC + BD + ACD001110Vy0kJ0p0k011101CD0010ABC + CD + AC + BD + ACD = AC + BC + BC + D(8) ACD+ ABCD+ AB(C+ D)+ D011110卜AA71JA0w寸Xzx00011110CD00ACD+ ABCD+ AB(C+ D)+ D= A+B+C+ D1-16(1) F1(A,B,C,D)= ? m(0,1,3,

23、4,5,9,10,14,15)厂A070000c0000011110CD 00 01 | 11 10F1(A,B,C,D) = AC+ ABD+ BCD + ABC+ ACD(2) F2(A, B,C,D) = ? m(2,3,6,8,913,15)00c000V0c00000011110CD 00 01 11 10F2(A, B,C,D) = ABC+ ACD + ABD+ ABC(3) F3(A,B,C,D) = ? m(0,2,4,6,8,10,13,15)000100p000c00011CD 00 01 11 101F3(A, B,C,D)= BD + AD + ABD(4) F4(A

24、, B,C,D)= ? m(0,1,2,3,5,7,9,10,13)C0J0011 ,000V000011110CD 00 01 11 10F4(A,B,C,D)= AB+ CD + BDC + AD(5) F5(A,B,C,D)= ? M (1,3,7,8,9,10,14)ABCD 00011110000111N00A0kyA000u010F5(A, B,C,D)= AD + BC+ ACD(6) F6(A,B,C,D)= ? M (3,4,7,8,11,12,15)F6(A,B,C,D) = CD+ CD + ABC(7) F7(A, B,C,D)= ? M (2,5,6,10,12,13

25、,14)00100010£V000011110CD00 01 11 10F7(A,B,C,D) = CD+ BC+ ACD(8) F8(A,B,C,D)= ? M (1,2,3,6,7,13,14,15)ABCD 0001111000A000001000011110F8(A, B,C,D)= CD + AB+ ABC1-17(1)FdA,B,C)= ? m(0,2,3,7)F1(A, B,C) = (B+ C)(A+ C)(2) F2(A,B,C,D)= ? m(0,1,7,8,10,12,13)F2(A, B,C,D)= (A+ B+ C)(A+ B+ C)(B+ C+ D)(A+

26、 C + D)(A+ B+ D)(3) F3(A,B,C,D)= ? m(1,2,3,7,8,9,12,14)F3(A, B,C,D)= (A+ C+ D)(A+ B+ D)(B+ C+ D)(A+ C+ D)(A+ B+ C)(4) F4(A,B,C,D)= ? m(0,2,5,7,8,10,13,15)F4(A,B,C,D)= (B+ D)(B+ D)(5) F5(A,B,C,D) = ? M (1,2,5,6,7,10,13,14)11代1301101 .111000011110CD 00 01 11 10F5(A, B,C,D)= (C+ D)(A+ C+ D)(B + C + D)(

27、A+ B+ D)(6) F6(A, B,C,D)= ? M (0,4,6,9,10,11,12,15)AB'CD 000111100061111011111r1A1101QF6(A, B,C,D)= (A+ C+ D)(B+ C + D)(A+ B+ D)(A+ B+ D)(A+ B+ C)(A+ C + D)(7) F7(A, B,C,D)= ? M (2,3,4,10,11,13,14,15)01111111c輕111110001110CD00 01F7(A,B,C,D) = (A+ B+ C+ D)(B+ C)(A+ C)(A+ B+ D)(8) F8(A,B,C,D)= ? M

28、(0,3,5,6,8,10,12,15)abP。！0111100011011©1®11A111011F8(代 B,C,D)= (B+ C + D)(A+ C + D)(A+ B+ D)(A+ B+ C+ D)=(A+ B+ C+ D)(A+ B+ C+ D)(A+ B+ C+ D)1-18约束条件 AB+ AC = 0(1) F1 = ABCD + ABCD + ABCD000000XXXXbl0X000111CDQ0 0111101F1 = BD(2) F2 = ABD+ ABD + BCD约束条件 AB+ AC= 0ABCDQO 0111 ip0卜0000Xk丿X70X

29、01111F2 = BD + BD约束条件BC+ CD = 0(3) F3 = BCD + BCD + ABCD11011100p0XQ0£0100010CD 00 01约束条件BD+ BD = 0F3 = BD + AD+ BD(4) F4 = ABCD + BCD + ABCDXfX丿0u丿X0X00X00011110CD 00 01 11 10F4 =BC AD约束条件ABCD + ABCD = 0(5) F5 = AC+ BD + ABC+ ABCD数字电路答案(5) F5(A,B,C,D)=邋m(2,4,6,7,12,15) +d(0,1,3,8,9,11)37ABCD 0

30、0011110约束条件? d(0,1,2,6) = 011XXAXH1100V01110000110CD 00 01F6 = B+ CD1-19(1)F1(A,B,C,D)=邋m(0,1,3,5,10,15)+d(2,4,9,11,14)1:XE丿0000广0X111000011110CD 00 01F5 = D + BC+ ACF1(A,B,C,D) = AB+ AC+ AC(6) F6 = AB+ BC+ CDA00000A£V000011110CD00 01 11 10F2(A,B,C,D) = BC+ AD+ CD+ ABCd(0,1,4,5,8,11)ABCDOO 0111

31、100001h代0xi00M00wV1110(3) F3(A,B,C,D)=邋m(2,6,9,10,13) +F3(A, B,C,D)= AD + CD + ABd(5,9,10,12,14,15)(4) F4(A,B,C,D)=邋m(1,3,7,11,13) +0厂00xA0xvxx0丿x00011110CD00 01 11 10F4(A,B,C,D)= d数字电路答案AB、0001111011 1 0 1 0F5(A, B,C,D)= CD + CD+ ADd(0,1,4,9,12,13)XXX00pXX010X£111000011110CD00 01(6) F6(A,B,C,D

32、)=邋m(2,3,6,10,11,14) +(8) F8(A,B,C,D)=邋m(0,4,8,11,12,15) +d(2,3,6,7,13)39d(0,1,2,4,8,15)CD0001一q1100X0:a001101111F6(A, B,C,D)= CD + BC F7(A,B,C,D)=邋m(3,5,6,7,10) +F7(A,B,C,D)= a+ bd数字电路答案AB 00011110F8(A, B,C,D)= CD+ CD第二章习题2- 1a) Z1 = AB + BC = B (A+ C)真值表：ABCF0 0 000 0 100 1 000 1 111 0 001 0 101 1

33、 011 1 11b) Z2 = A+ BC + D = ABCD真值表：ABCDFABCDF00001100000001010010001001010000110101100100011000010101101001100111000111011110c) Z3= c+ D+ B+ A? E C+ D+ B+ALJE=(C+ D)LB+ A_ E真值表：ABCDEF000000000011000101000110001001001010001101001110ABCDEF010000010011010100010111011000011011011100011111ABCDEF1000011

34、00010100101100110101001101010101101101110ABCDEF1100011100101101011101101110011110101111011111102- 2a）表达式：Z = B+ CAC A? B C? A ABC 排(BC ) A真值表:ABCF0 0 010 0 110 1 010 1 111 0 011 0 101 1 001 1 10X = B 排 C Ab）表达式：Y = AB + BC + AC真值表:ABCXY00000001110101101101100101010011000111112- 3表达式：z= adbbcdaDC = B

35、CD真值表：41数字电路答案ABCDZABCDZ00001100010001110011001001010000111101110100111001010111101101101111010111111111波形图:3)432- 41)2)数字电路答案4)5)F6)F6=(B+ CD)AB + E = EB+(A+ B)CDEABDEFC2- 51) F = ABCD65AD 1 P2)F = ABC ADF3)f = Acdbcd4)F = ACACBDBD5)F = ABBCCAF6)F = ABBCC AF2-61) F = A+ B+ C + DABCD2) F 二 A+D+B+CAB

36、CD3) F = A+ C + B+ D+ C + A+ C+ A+ DABCDF4) F = A+ B + A+ B + C + D + C + DDBAF5) F = A + B + B + C + C + AF6)F= A + B+C + A+ D0101101001011010000111102-7(1)卡诺图及表达式:CD 00 01 11 10F = (A+ B+ C+ D)(A+ B+ C+ D)(A+ B+ C + D)(A+ B+ C + D)(A+ B+ C + D)(A+ B+ C + D)(A+ B+ C + D)(A+ B+ C+ D)(2 )电路图：A B C D2- 8(1 )真值表:S2SiSoABF000001000010