?(A?B)C
?(A?B?C)AB?BC?CA
得证。
（4）A?B?C?ABC
证明： 等式右侧
?ABC?(A?B?C)?AB?BC?CA
?ABC?A?AB?BC?CA?B?AB?BC?CA?C?AB?BC?CA ?ABC?A?B?BC?C?B?A?C?AC?C?AB?B?A?ABC?A?B?C?B?A?C?C?B?A ?ABC?ABC?ABC?ACB
（AB?AB)?C 等式左侧?
?（AB?AB)C?(AB?AB)C ?（AB?AB)C?(AB?AB)C
?ABC?ABC?ABC?ABC ?ABC?ABC?ACB?A?B?C 比较左右两侧，得证。 （5）ABC
证明：
（AB?AB)?C 等式右侧?
?（AB?AB)C?(AB?AB)C ?（AB?AB)C?(AB?AB)C
?ABC?ABC?ABC?ABC
得证。
（6）A(C?D)?BCD?ACD?ABCD?C?D
证明： 等式左侧
?A(CD?CD)?(B?AB)CD?ACD
?A(CD?CD)?(A?B)CD?ACD
?A(CD?CD)?ACD?BCD?ACD ?A(CD?CD)?A(CD?CD)?BCD
?CD?CD?BCD
?CD?(1?B)CD
?CD?CD
?C?D
得证。
2.6 根据对偶规则，求出下列函数的对偶。
（1）L?
A(B?C)?A(B?C)
解：L??(A?BC)(A?BC)
（2）L?A(B?C)?AB(C?D)?ABC?D
解：L??(A?BC)(A?B)CD?(A?B?C)?D
（3）L
?AB?BC?CA
解：L??(A?B)(B?C)(C?A)
（4）L?(A?C)(A?B?C)(B?C)(A?B?C)
解：L??AC?ABC?BC?ABC
2.7 根据反演规则，求出下列函数的反函数
（1）L?(A?BC)DE
解：L?A?BC?DE
（2）L?[A?(BC?CD)E]F
解：L?A?(BC?CD)E?F （3）L
?A?B?CD?C?D?AB 解：L?(A?B?CD)(C?D?AB)
（4）L?AB?ABC(A?BC)
解：L?AB?ABC另解：（1）L（2）L（3）L（4）L?A?BC
?A?B?C??D?E ??F ?A?B?CC?D?E???????AB?C?D??CD??A?B? ?A?B?A?B?C??A?B?C?
2.8 将下列函数变换为最小项之和的表达式
（1）L?AB?AC?BC
解：L?AB(C?C)?AC(B?B)?BC(A?A)
?ABC?ABC?ABC?ABC?ABC?ABC
L?ABC?ABC?ABC?ABC??m?3,5,6,7?
（2）L?BC?AB?AC 解：L?BC(A?A)?AB(C?C)?AC(B?B)
?ABC?ABC?ABC?ABC?ABC?ABC
L?ABC?ABC?ABC?ABC?ABC?ABC??m?0,1,3,4,6,7?
（3）L?(A?B)AB?BC
?(A?B)(AB?BC)
?(A?B)(A?B)(B?C)
?(A?A?A?B?AB?B?B)(B?C) ?(A?B?AB)(B?C)
?(A?B?AB)(B?C)
?A?B?B?AB?A?B?C?ABC ?AB?ABC?ABC
?AB(C?C)?ABC?ABC
?ABC?ABC?ABC
L?ABC?ABC?ABC??m?3,4,5?
（4）L?(A?B?C)?A?B?C （A?B）C 解：L?(A?B?C)??A?B?C?AC?BC
?A(B?B)?B(A?A)?C(A?A)?AC?BC
?AB?AB?AB?AB?AC?AC?AC?BC ?AB?AB?AB?AC?AC
?AB(C?C)?AB(C?C)?AB(C?C)?AC(B?B)?AC(B?B)?ABC?ABC?ABC?ABC?ABC?ABC?ABC?ABC?ABC?ABC?ABC?ABC?ABC?ABC?ABC?ABC?ABC
L?ABC?ABC?ABC?ABC?ABC?ABC?ABC??m?1,2,3,4,5,6,7?
2.9 用卡诺图化简下列逻辑函数为最简与或表达式 (1)
L?AB?BC?AC?BC 解：直接在卡诺图上填写对应的各项。如图2.9-1所示。
图2.9-1
(2)
L?B?AC
L?AC?AC?BC?BC
解：直接在卡诺图上填写对应的各项。如图2.9-2所示。
图2.9-2
化简结果：L?AB?AC?BC
(3) L?AB?BD?BCD?ABCD 解：直接在卡诺图上填写对应的各项。如图2.9-3所示。
图2.9-3