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逻辑代数与硬件描述语言基础
逻辑变量 逻辑代数 基本定律和定理 逻辑函数及其化简
2.1 逻辑代数
2.1.1 逻辑代数的基本定律和恒等式
基本定律
0-1律： a 0 a
a0 0 a a 1 aa a aa 0
( a b) c a ( b c)
a 1 1 a a a a a 1
结合律：
a a
( a b) c a ( b c)
交换律： a b b a
a b b a
a (b c) a b a c 分配律： a b c ( a b) ( a c )
反演律（摩根定律）：
a b c a b c a b c a b c 真值表证明法：
例：证明 a b a b
a 0 0 1 1 b 0 1 0 1 a b 1 1 0 1 0 1
， ab
a b
a+b 0+0=1 0+1=0 1+0=0 1+1=0
a b
1 0 0 0
ab
0· = 1 0 0· = 1 1 1· = 1 0 1· = 0 1
a+b 1 1 1 0
0 0
吸收律： (1)
a a b a
(3) a a b a b (4) ( a b) ( a c ) a bc
(2) a ( a b)
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向豆丁求助：有没有LAQ?
