1 × × 1
0 LA?A?A?B1?B2?A?B1?B2 LB?LA?A?B1?B2?A?B1?B2?
____________________3.1.2 用逻辑代数证明下列不等式 (a)
A?AB?A?B
A?BC?(A?B)(A?C)，得
由交换律 (b)
A?AB?(A?A)(A?B)?A?B
ABC?ABC?ABC?AB?AC
ABC?ABC?ABC?A(BC?BC?BC)?A(C?BC)?A(C?B)?AB?AC (c)
A?ABC?ACD??C?D?E?A?CD?E
A?ABC?ACD??C?D?E?A?ACD?(C?D)E_____?A?CD?CDE?A?CD?E3.1.3 用代数法化简下列等式 (a)
AB(BC?A)
AB(BC?A)?ABC?AB?AB (b) (A?B)(AB)
(A?B)(AB)?AB
(c) (d)
_______ABC(B?C)
_______ABC(B?C)?(A?B?C)(B?C)?AB?BC?AC?BC?C?AB?C_____
A?ABC?ABC?CB?CB_____
A?ABC?ABC?CB?CB?A?C
(e) (f)
____________________________AB?AB?AB?AB____________________________
_________AB?AB?AB?AB?A?A?0____________________________________________________________________________
(A?B)?(A?B)?(AB)?(AB)
___________________________________________________________________________________________________________(A?B)?(A?B)?(AB)?(AB)?(A?B)?(A?B)?(AB)?(AB)?(AB?BA?B)(AB?AB)?B(AB?AB)?AB
(g) (h)
(A?B?C)(A?B?C) (A?B?C)(A?B?C)?A?B
ABC?ABC?ABC?A?BCABC?ABC?ABC?A?BC?A?ABC?BC?A?BC?BC?A?C_____________________________ (i)
AB?(A?B)
__________AB?(A?B)?AB?(A?B)?(A?B)(A?B)?A?B
________________________ (j)
B?ABC?AC?AB
(k)
B?ABC?AC?AB?B?ABC?AC?B?AC?ACABCD?ABD?BCD?ABCD?BC
(l)
__________________________________________________ABCD?ABD?BCD?ABCD?BC?ABC?ABD?B(CD?C)?ABC?ABD?B(C?D)?ABC?ABD?BC?BD?B(AC?AD?C?D)?B(A?C?A?D)?AB?BC?BD__________________________________________________AC?ABC?BC?ABC
____AC?ABC?BC?ABC?(AC?ABC)?(B?C)?(A?B?C)?(ABC?ABC)(A?B?C)?BC(A?B?C)?ABC?BC?BC (m)
______________________________________________AB?ABC?A(B?AB)
____________________________________________________________________________________________________AB?ABC?A(B?AB)?___________________________________A(B?BC)?AB?AB_
____________________________?A(B?C)?A?A?B?C?A?03.1.4 将下列各式转换成与 – 或形式
(a)
__________________A?B?C?D________
__________(1)当A?B?0，C?D?1时，真值为1。于是
AB=01，CD=00或CD=11时，真值为1； AB=10，CD=00或CD=11时，真值为1。
则有四个最小项不为0，即ABCD、ABCD、ABCD、ABCD
(2)当A?B________?1，C?D?0时，真值为
__________1。
AB=00，CD=10或CD=01时，真值为1；
AB=11，CD=10或CD=01时，真值为1。
则有四个最小项不为0，即ABCD、ABCD、ABCD、ABCD (b)
___________________________________A?B?C?D?_________________________________?m(1,2,4,7,8,11,13,14)
_________________________________A?B?C?D?C?D?A?D_________________________________________________
A?B?C?D?C?D?A?D?(A?B)(C?D)?(C?D)(A?D)?(C?D)(A?B?D)?AC?AD?BC?BD?CD?D?AC?BC?D______________________________________________________________________ (c)
AC?BD?BC?AB
__________________________________________________________________________________________AC?BD?BC?AB?AC?BD?BC?AB?(A?C)(B?D)?(B?C)(A?B)?AB?BC?AD?CD?AB?AC?B?BC?B?AD?CD?AC
3.1.7 利用与非门实现下列函数
(a) L=AB+AC (b)
_______________________L?AB?AC_____________
L?D(A?C)
(c)
_____________________________L?D(A?C)?DACL?(A?B)(C?D)
________________________________________
______________________L?(A?B)(C?D)?ABCD
3.2.2 用卡诺图法化简下列各式 (a)
______________________AC?ABC?BC?ABC____________
_____________________________AC?ABC?BC?ABC?AC?BC?BC?ABC___________
?AC?C?ABC?C?ABC?C(b)
ABCD?ABCD?AB?AD?ABC
ABCD?ABCD?AB?AD?ABC?AB?ABCD?AD?A(B?BCD)?AD?AB?ACD?AD?AB?A(D?DC) ?AB?AD?AC(c) (AB?BD)C?BD(AC)?D(A?B)
____________________________________(AB?BD)C?BD(AC)?D(A?B)
?ABC?BCD?BD(A?C)?DAB?ABC?BCD?ABD?BCD?ABD?ABC?BCD?AB?BCD
(d) ABCD?D(BCD)?(A?C)BD?A(B?C)
____________________ABCD?D(BCD)?(A?C)BD?A(B?C)
?ABCD?BCD?ABD?BCD?ABC?m11?m1?m9?m12?m14?m6?m14?m4?m5?
?m(1,4,5,6,9,11,12,14)