数字电子技术基础(第3版)-李庆常-王美玲-课后习题答案

1第2222章逻辑代数及其化简2-1分别将十进制数29.625，127.175和378.425转换成二进制数。解答：(29.625)10=(1,1101.101)2(127.175)10=(111,1111.0010,1100,…)2(378.425)10=(1,0111,1010.0110,1100,…)22-2分别将二进制数101101.11010111和101011.101101转换成十进制数。解答：(101101.11010111)2=(45.83984375)10(101011.101101)2=(43.703125)102-3分别将二进制数100110.100111和101011101.1100111转换成十六进制数。解答：(100110.100111)2=(0010,0110.1001,1100)2=(26.9C)16(101011101.1100111)2=(1,0101,1101.1100,1110)2=(15D.CE)162-4分别将十六进制数3AD.6EBH和6C2B.4A7H转换成二进制数。解答：(3AD.6EB)16=(11,1010,1101.0110,1110,1011)2(6C2B.4A7)16=(110,1100,0010,1011.0100,1010,0111)22-5试用真值表法证明下列逻辑等式：(1)ABACBCABC++=+(2)ABABBCABABAC++=++(3)ABBCCAABBCCA++=++(4)ABABBCACABC+++=+(5)ABBCCDDAABCDABCD+++=+(6)ABABABCAB++=+证明：(1)ABACBCABC++=+2真值表如下所示：ABCABACBC++ABC+0000000111010000111110000101111101111111由真值表可知，逻辑等式成立。(2)ABABBCABABAC++=++真值表如下所示：ABCABABBC++ABABAC++0000000100010110111110011101111100011111由真值表可知，逻辑等式成立。(3)ABBCCAABBCCA++=++真值表如下所示：ABCABBCCA++ABBCCA++00000001110101101111310011101111101111100由真值表可知，逻辑等式成立。(4)ABABBCACABC+++=+真值表如下所示：ABCABABBCAC+++ABC+0001100111010110111110000101001100011111由真值表可知，逻辑等式成立。(5)ABBCCDDAABCDABCD+++=+真值表如下所示：ABCDABBCCDDA+++ABCDABCD+0000110001000010000011000100004010100011000011100100000100100101000101100110000110100111000111111由真值表可知，逻辑等式成立。(6)ABABABCAB++=+真值表如下所示：ABCABABABC++AB+0001100111010110111110011101111100011100由真值表可知，逻辑等式成立。2-6求下列各逻辑函数F的反函数F和对偶式F¢:(1)1FAABCAC=++(2)2()()()FABAABCABCABABC=++++++5(3)3FABCDADB=+++(4)4FABBDCABBD=+++++(5)()()5FABABBCBC=++(6)6FCDCDACDB=+++解答：(1)1FAABCAC=++1()()FAABCAC=+++1'()()FAABCAC=+++(2)2()()()FABAABCABCABABC=++++++2()()()FABAABCABCABABC=+++++++2'()()()FABAABCABCABABC=+++++++(3)3FABCDADB=+++3FABCDADB=+++3'FABCDADB=+++(4)4FABBDCABBD=+++++4()()()FABBDCABBD=+++4'()()()FABBDCABBD=+++(5)()()5FABABBCBC=++5()()()()FABABBCBC=+++++5'()()()()FABABBCBC=+++++(6)6FCDCDACDB=+++6()()()()FCDCDACDB=++++66'()()()()FCDCDACDB=++++2-7某逻辑电路有A、B、C共3个输入端，一个输出端F，当输入信号中有奇数个1时，输出F为1，否则输出为0，试列出此逻辑函数的真值表，写出其逻辑函数表达式，并画出逻辑电路图。解答：由题意可列出真值表如下：ABCF00000011010101101001101011001111由真值表可以得到函数表达式为：FABCABCABCABC=+++逻辑电路如图T2-7所示：ABCABCABCABCF图T2-72-8设计一个3人表决电路，要求：当输入A、B、C中有半数以上人同意时，决议才能通过，但A有否决权，如A不同意，即使B、C都同意，决议也不能通过。解答：定义变量A、B、C，1代表同意，0代表不同意；F为结果，1代表通过，0代表不能通过。由题意可列出真值表如下：7ABCF00000010010001101000101111011111由真值表可以得到函数表达式为FABCABCABC=++，化简可以得到FACAB=+。2-9试用代数公式法证明题2-5中的各等式。（1）ABACBCABC++=+证明：()ABACBCABABCABABCABC++=++=+=+（2）ABABBCABABAC++=++证明：()ABABBCABBCABABBCACABABABAC++=++=+++=++（3）ABBCCAABBCCA++=++证明：()()()()()()ABBCCAABBCBCCAABCAABBCCACAABBCABCABCABBCCACABCABABBCCA++=+++++=+++++=++++++++=++（4）ABABBCACABC+++=+证明：(1)ABABBCACABCACACBCABC+++=++=++=+8（5）ABBCCDDAABCDABCD+++=+证明：()()()()()()ABBCCDDAABBCCDDAABACBCCDCADAABCDABCD+++=++++=++++=+（6）ABABABCAB++=+证明：()()ABABABCABABABCAABCABBAB++=+++=+++=+2-10证明下列异或运算公式：(1)0AA?(2)1AA?(3)0AA?(4)1AA?(5)ABABA?(6)ABAB??解答：（1）0AA⊕=证明：000AAAAAA⊕=+=+=（2）1AA⊕=证明：11101011AAAAA⊕=+=+=+=iiii（3）0AA⊕=证明：00010AAAAAA⊕=+=+=iiii（4）1AA⊕=证明：91AAAAAAAAAAAA⊕=+=+=+=（5）ABABA⊕=证明：()()ABABABABABABABABABABABABA⊕=+=+++=+=ii（6）ABAB⊕=⊕证明：()()ABABABABABABABABABABABABABAB⊕=+=+=+==++=+=⊕2-11用公式法化简下列逻辑函数为最简与或式：(1)1()FABABABABCD=+++(2)2FABCACABCAC=+++(3)3()()FABABABAB=++(4)4()()FAABABCC=+++(5)5()FABACDBCD=+++(6)6()()()FABAABCABCABABC=++++++解答：（1）1()FABABABABCD=+++化简：1()()()()FABABABABCDAABABCDABABCDABABCDAB=+++=++=++=+=（2）2FABCACABCAC=+++化简：2()()()()FABCACABCACABCCABCACABCABCACABCABCACABCACABCACABCABCACABCABACACABCABAABCAABC=+++=+++=+++=++=⊕+=+=+++=+++=++=+=+⊙10（3）3()()FABABABAB=++化简：3()()()000FABABABABABABABABABABAB=++=+=+=+=（4）4()()FAABABCC=+++化简：4()()()()()0FAABABCCABABCABABC=+++=+++=+=（5）5()FABACDBCD=+++化简：5()()()()()()()()()()()()FABACDBCDABACDBCDAAACADABBCBDBCDACABBCADBDBCDACABADBDBCDACABADBCDABCACACDABABCABDABDACDADACABAD=+++=+++++=+++++++=++++++=+++++=++++=++++++++=++（6）6()()()FABAABCABCABABC=++++++化简：6()()()()FABAABCABCABABCAABCABCABABCACABCABABCABCABABBCABC=++++++=+++++=++++=++=++=++2-12用卡诺图化简下列逻辑函数为最简与或式：(1)1(3,5,6,7)Fm=å(2)2(4,5,6,7,8,9,10,11,12,13)Fm=å(3)3(2,3,6,7,10,11,12,15)Fm=å(4)4(1,3,4,5,8,9,13,15)Fm=å11(5)5(1,3,4,6,7,9,11,12,14,15)Fm=å(6)6(0,2,4,7,8,9,12,13,14,15)Fm=å解答：（1）13,5,6,7Fm=∑（）卡诺图：BCA000111100001010111由卡诺图可知：13,5,6,7FmACABBC==++∑（）（2）24,5,6,7,8,9,10,11,12,13Fm=∑（）卡诺图：CDAB00011110000000011111111100101111由卡诺图可知：24,5,6,7,8,9,10,11,12,13FmABABAC==++∑（）（3）32,3,6,7,10,11,12,15Fm=∑（）卡诺图：CDAB0001111000001101001111101010001112由卡诺图可知：32,3,6,7,10,11,12,15FmABCDACBCCD==+++∑（）（4）4134,5,8,9,13,15Fm=∑（，，）卡诺图：CDAB00011110000110011100110110101100由卡诺图可知：4134,5,8,9,13,15FmABDABCABDABC==+++∑（，，）（5）5134,6,7,9,11,12,1415Fm=∑（，，，）卡诺图：CDAB00011110000110011011111011100110由卡诺图可知：5134,6,7,9,11,12,1415FmBDBDCD==++∑（，，，）（6）6024,7,8,9,12,13,14,15Fm=∑（，，）卡诺图：CDAB0001111000100101101011111113101100由卡诺图可知：6024,7,8,9,12,13,14,15FmABACCDABCBCD==++++∑（，，）2-13对具有无关项0ABAC+=的下列逻辑函数进行化简：(1)1FACAB=+(2)2FACAB=+(3)3FABCABDABDABCD=+++(4)4FBCDABCDABCABD=+++（5）5FACDABCDABDABCD=+++(6)6FBCDABCDABCD=++解答：（1）1FACAB=+1FACABACABABACACBAC=+=+++=++（2）2FACAB=+解：2FACABACABABACBC=+=+++=+（3）3FABCABDABDABCD=+++3FABCABDABDABCDABACABCABA