数字电路与逻辑设计课后习题测验答案蔡良伟第三版.docx

1、数字电路与逻辑设计课后习题测验答案蔡良伟第三版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%16210(2)10810 = 1*8 + 5*8 + 4*8 = 15481548 = 1 5 4 = 110110Q001101100110110C2 = 01101100= 6C166 C10 - 1(3)13.12510 = 1*8 1 + 5*8 0 + 1*8 1 = 15.1815.18 = 1 5. 1 = 1101.0012001101 0011101.00!

2、 = 1101.0010= D26D 2210 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.A168 3 A1-2(1)1011012 =101101= 5585 51011012 =00101101= 2D162 D558 = 5*8+ 5*8 0 = 4510(2)11100101=011100101= 34583 4 51110010! = 11100101= E516E 5345

3、8 = 3*8 2 + 4*8 1 + 5*8 0 = 229(3)101.0011= 101.001100= 5.1485 1 4101.001!= 0101.0011= 5.365 35. 14= 5*H8 1 *+8 - 4=* 8 5o 1 87 5(4)100111.101 = 100111.101= 47.44 7 4100111.101 = 00100111.1010= 27A162 7 A1 0 147.54* 8 7*80 5*8 -39.625101-3(1)168 = 1*8 1 + 6*8 0 = 1410168= 1 6 = 111020011101110= 11=低

4、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.AC1631 A C2 10 1 2(4)126.748 = 1*8 + 2*8 + 6*8 + 7*8 -

5、+ 4*8 - = 86.937510126.74 = 1 2 6. 7 4 = 1010110.1111001 010110 1111001010110.1111= 01010110.1111= 56.F165 6 F1-4(1)2人6= 2 A = 1010102001010101010102 = 101010= 5285 2(2)B2F16 = B 2 F = 1011001011111011 00101111101100101111= 101100101111= 545785 4 5 754578 = 5*8 3 + 4*8 2 + 5*8 1 + 7*8 0 = 286310(3)D

6、3.E16= D 3 . E = 11010011.1111101 0011 111011010011.111= 011010011.111= 323.7832 3 72 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= 703.76287 0 3 7 6 22 1 0 . 1 . 2 3703.7628= 7*8 + 0*8 + 3*

7、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。(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00011001110

8、10110111110011101111101111111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 CD 二 A ACD

9、 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 + ABC(7)ABD +

10、 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 CD=AB BC CD AB

11、 BC CD AD DA=AB BC CD DA Ab BC CD AD=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 = AC+ BDC + A

12、+ 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 = BC + CDB (AD+ C)F6= (B+ C)(C+

13、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 B CF0 0 010 0 100 1 000 1 111 0 001 0 111 1 001 1 110001111010100110(2) F2 = a+ bc+ cdABCFDABCFD000(P100100000

14、110011001001011000111101110100011010010011101101110111100111111111CD00000111100111100010001111111111(3) F3 = AB+ B(C+ AD)ABCDFABCDF00000100000001010011、CD0001001ABC 0001111011100001100111101110100111000011111010111101011000001101111001001110111111110(4)F4 = (A+ B+ C)(A+ B+ C)(A+ B+ C)BC00 01 11 1011

15、100011(5)F5 = (BD+ C)(C+ AD)ABCDABCD000010000000100100101011000111011010011000100110001101111001111111CD00 01 11 10000111100011001100110111(6) F6 = (AB+CD)(BC+ DA)(AC+ BD)ABCDABCD0000100000001000001010100010101001001100010011000110111001101110CD 00 01 11 10000111100000000000000000(7) F7 = A+ BC+ BA

16、+ C + DABCF 1)ABCFD0001(100100001 1100110010 (101100010 1101110100 (110100100 1110110110 (111100111 111111(8) F8 二 AbD BC CAD D AC BDABCDFABCDFd C 0 0110 0 010 0 0 11I D 0 110 0 101L 0 1 010 0 11110 1110 1 0 01L 1 0 010 10 11110 110 1101111000 1110111101-10标准与或式:110000101111111111100001111001CD0000c

17、o11111011100111011110011110F =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 = 10,1,3,4,5,8,10,11,12,13,14,15(7)F7 八 0,2,5,6(8)F81

18、,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 10,2,4,5,7,8,9,13,14,15(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

19、= 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+ (A+ C)(D + A+ B)+ (C + D)E(6)= AB + AD + CD + ABC + CDE=AB+ AD + CD+ BC+ EC+ A

20、BCD + 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|Xy01100uK0VX0001111001CD00ABC+ BC+ AD+ CD = BC+ AC+ D(3)Abc+ abCd+ ABCD+ ACh00R00w0000000111100

21、1 11 100000J匚clLx00ABC+ ABCD+ ABCD+ AC = AB+ AC + BCD + BCD(4)B(C+ AD)+ AC(B+ D)CDAB 、00 01 11 1000011110B(C+ AD) + AC(B+ D)= AB+ AC+ BD(5)B(C? D) ACD + BCD + BCDAB000八000110h00y0V0000011110011110B(C ? D) ACD + BCD + BCD = CD + BCD(6) ABC + BCD + AD+ A(B + CD)ABC+ BCD + AD+ A(B+ CD)= ABD + ABD + AC(

22、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(0,1,3,4,5,9,10,14,15)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, B,C,D)= ? m(0,1,2,3,5,7,9,10,13)C0J0011 ,000V000011110CD 00