《数字电路逻辑设计》逻辑函数及其化简练习题

1、实用文档数字电路逻辑设计练习题逻辑函数及其化简 一.用公式证明下列各等式。1. AB AC (B C)D AB AC D 原式左边=ab Ac Bd Cd =AB Ac+bc+BCd =AB AC+D=右边2. A c A B A C d+bc A bc 原式左边 A c(i+d)+A b+bc =A c+A b+bc=Ac+B)+bc =A BC+bc=A+bc=右边3. BCD BCD ACD+ABC D+A BCD +bc d+bcd bc bc+bd原式左边=bcd+A BCD bCd+bcd +Abc d+bc d+acd=bcd+A bcd+bd+bc d+acd =bcd+acd

2、+Bcd+bd+b d =bcd+acd+bd+dc+b d =bcd+bd+dc+bC d=C (D+B) + B (D+0 =bc+bd+bc=右边2. F=AB+AB+BC =m (2,3,4,5,7 )F m(0,1,6) F*= m(1,6,7)3. f=ab+c bd+A d b c =m (1,5,6,7,8,9,13,14,15)F m(0 23,4,10,11 ,12 ) F*=m(3,4,5,11,12,13,15)三.用公式法化简下列各式1. f=abc+a cd+ac =A(BC+C)+A CD=AC AB A CD =C(A ad) ab=aC+CD+aeT2. f=

3、aC D+bc+bd+aB+AC+eT C =ac d+bc+bd+aB+ac+bc+b- c =ac d+bc+Ac+b=ad+c+B"3. F=(A+B)(A+B+C)(A+C)(B+C+D) "f*= ab+abc+ac+bcd=ab+ac+bcd=ab+acF=(F*)*=(A+B)(a+c)=AC+AB 4. AB B+D CD+BC+A BD+A+CD=1原式左边二届 B+d Cd Bc+a bd A+c+d=(ab+ b+d+Cd)(B+c-)+c+d=(B+D)(B+C) +c+d=bc+bd+cd+c+D=i=右边二.写出下列各逻辑函数的最小项表达式及其对

4、偶式、 反演式的最小项表达式4. F=AB+A B?BC+B CF AB+A B BC+B C ab+a b bc+b C ACAB BC B C AC AB B C AC5. F=AC+BC B(AC AC)F (A C)(B C) ABC ABCAB A C BC C ABC ABCAB C (A B)C AC BC1. f=abcd+acd+bd = m (4,6,11,12,14,15 )四.用图解法化简下列各函数。F m(0,1,2,3,5,7,8,9,10,13) F*= m(2,5,6,7,8,10,12,13,14,15)F= m(8,9,10,11)m(1,5,9,13)m(

5、8,9,12,13) CD AB AC2. F=(A+B)(A+B+C)(A+C)(B+C+D)F m(4,5)m(6,14)m(13,15)ABC BCD ABDF m(0,1,4,5,8,9,12,13) m(5,7,13,15) m(0,3,8,10)C BD B DCD00011110000：1 ：J 100010：1 i u j00110X 1-1 一一门100:1 ;:11 j -F = Em (4, 5, 6, 7) +Em (10, 11, 14, 15)F(A,B,C,D) m(0,1,4,7,9,10,15) 6. d(2,5,8,12,13)=Ab+ac3. F(A,B,C,D)药(0,1,3,5,6,8,10,15)%B CD0001111000101卜111L1 .10的F = Em (0, 1) +Em (1, 3) + Em (1, 5) +Em (8, 10) +12 m (6) +E m (15)F(A,B,C,D) m(4,5,6,13,14,15)f=A B C+A Bd+A Cd ab d Abcd abcd4. F(A,B,C,D)=