习题答案 第一章
1.(a) F1?AB?BC?AC
(b) F2?((A??B?)??AB)??(AB?AB)??(AB)??A??B? (c) Y1?A?B?C?A?B?C?A?BC??AB?C??ABC
Y2?((AB)?((A?B)C)?)??AB?(A?B)C?AB?A'BC?AB'C?B(A?A'C)?AB'C?B(A?C)?AB'C?AB?BC?AB'C?A(B?B'C)?BC?A(B?C)?BC?AB?AC?BC2.(1)真值表如题表1-1所示：
题表1-1
A 0 0 1 1
B 0 1 0 1
AB'?A'B (A'?B')(A?B) 0 1 1 0
0 1 1 0
由表可知等式成立。
(2)真值表如题表1-2所示：
题表1-2
A 0 0 0 0 1 1 1 1
B 0 0 1 1 0 0 1 1
C 0 1 0 1 0 1 0 1
ABC?ABC'?AB'C 0 0 0 0 0 1 1 1
AB?AC 0 0 0 0 0 1 1 1
由表可知等式成立。
3.(1) F1'?(CD?A'B')'?(CD)'(A'B')'?(C'?D')(A?B)?AC'?AD'?BC'?BD'
F1?(C?D)(A'?B')?A'C?A'D?B'C?B'D
(2) F2'?((A'?B)(C'?D)')'?(A'?B)'?(C'?D)?AB'?C'?D
DF2?A'B?(C'D)'?A'B?C?D'
(3) F3'?((A'?B)'(B'?C)?(D'E)')'?((A'?B)'(B'?C))'?D'ED?(A'?B?(B'?C)')?D'E?(A'?B?BC')D'E?(A'?B)D'E?A'D'E?BD'EF2(A,B,C,D)?(A'B'?ABC)'(B?CD)?(A'B')'(ABC)'(B?CD)?(A?B)(B?CD)(A'?B'?C')?(AB?ACD?B?BCD)(A'?B'?C')?(B?ACD)(A'?B'?C')?A'B?BC'?AB'CD?A'BCD?A'BC'D'?A'BC'D?A'BCD'?ABC'D?A'BC'D'?A'BC'D??ABC'D'?AB'CD?A'BCD?A'BC'D'?A'BC'D?A'BCD'?ABC'D?ABC'D'?AB'CDF3?(A,B,C)?(AB?B'C?AC)'?(AB?B'C)'?(AB)'(B'C)'DF3?((A'B)'?B'C)(D'?E)'?(A?B'?B'C)DE'?(A?B')DE'?ADE'?B'DE'?(A'?B')(B?C')?A'B?A'C'?B'C'?A'B?B'C'?A'BC?A'BC'?AB'C'?A'B'C'
4.(1) F1(A,B,C)?AB?A'C?AB(C?C')?A'C(B?B')?ABC?ABC'?A'BC?A'B'C （2）
F2?AB'?BC'D?C'D'?ABC'?AC'D?A(B'?BC'?C'D)?C'(BD?D')
（3） ?A(B'?C'?C'D)?C'(B?D')?AB'?AC'?BC'?C'D'?AB'?BC'?C'D'
5.(1) 右边=A'A?A'B?AB'?B'B?A'B?AB'=左边
等式成立。
（2） 左边=AB(C?C')?AB'C?AB?AB'C?A(B?B'C)?A(B?C)?AB?AC=右边
等式成立。
（3）左边=(A?C')(B?BD?BD'?DD')?(A?C')B?AB?BC'=右边
等式成立
6.（1）F1?AB?AC?A'B?BC'?B(A?A')?AC?BC'?B?AC?BC'?AC?B （2）
（3）
（4） 7.(1)
CDAB00001011111100010110110101100101
F1?A'D?C'D?A'B'C'?ACD'
(2)
F3?AB'?(A'C?B'C)'?AB'?(A'C)'(B'C)'?AB'?(A?C')(B?C')?AB'?(AB?AC'?BC'?C')?AB'?AB?C'?A?C'F4?((AB'?A'B)'C?AB'C)(AD?BC)?((A'B'?AB)C?AB'C)(AD?BC)?(A'B'C?ABC?AB'C)(AD?BC)?ABCD?AB'CD?ABC?ABC?AB'CD?AC(B?B'D)?AC(B?D)?ABC?ACDCDAB00000010110101010101110011(3)
8.(1)
(2)
100100
F2?A'BC'D?AB'C'D?A'CD'?ABCCDAB00011110001000011101111110101100
F3?C'D'?BC'?AC'?A'BD'?ABD
ABC000111100001110110
F1?A'B?AC?((A'B)'(AC)')'