布尔代数定律_布尔代数的公理和定律
布尔代数定律
A+A =A Boolean Algebra differs from both general mathematical algebra and binary number systems. In Boolean Algebra, A+A =A
A.A = A, becau the variable A A has only logical value. It doesn't have any numerical significance. In ordinary
简单回答and A.A = A
A.A = A2, becau the variable A A has some numerical value here. Also, in Binary mathematical algebra, A+A = 2A
A+A = 2A and A.A = A2
Boolean Algebra 1+1 = 1 itlf. Unlike
1+1 = 2 but in Boolean Algebra 1+1 = 1
1+1 = 10, and in general mathematical algebra 1+1 = 2
Number System 1+1 = 10重庆旅游景点大全
AOI (AND, OR ordinary algebra and Binary Number System here is subtraction or division in Boolean Algebra. We only u AOI (AND, OR and NOT/INVERT) logic operations to perform calculations in Boolean Algebra.
and NOT/INVERT)
AA = A ，因为变量A A仅具有逻辑值。 它没有任何数值布尔代数不同于⼀般的数学代数和⼆进制数系统。 在布尔代数中， A + A = A
A + A = A且AA = A
AA = A2 ，因为变量A A在此处具有某些数值。 同样，在⼆进制数系统1 + 1 = 10中
1 + 1 = 10中 ，
A + A = 2A且AA = A2
意义。 在普通的数学代数中， A + A = 2A
布尔代数1 + 1 = 1中 。 与普通代数和⼆进制数系统不同，布尔代数是减法或除法。 我们仅使
1 + 1 = 2中，但在布尔代数1 + 1 = 1中
通常在数学代数1 + 1 = 2中，
AOI(AND，OR和NOT / INVERT)逻辑运算来执⾏布尔代数中的计算。
⽤AOI(AND，OR和NOT / INVERT)
布尔代数中的公理 (Axioms in Boolean Algebra)
There are some t of logical expressions which we accept as true and upon which we can build a t of uful theorems.
An axiom is nothing more
Axioms or postulates of Boolean Algebra. An axiom is nothing more The ts of logical expressions are known as Axioms or postulates of Boolean Algebra
西藏歌曲
than the definition of three basic logic operations (AND, OR and NOT). All axioms defined in boolean algebra are than the definition of three basic logic operations (AND, OR and NOT)
the results of an operation that is performed by a logical gate.
我们接受了⼀些逻辑表达式，这些逻辑表达式是正确的，并且可以在这些逻辑表达式上建⽴⼀组有⽤的定理。 这些逻辑表达式集被称为布
布公理只不过是三个基本逻辑运算(AND，OR和NOT)的定义 。 布尔代数中定义的所有公理都是由逻辑门执⾏尔代数的公理或假设 。 公理只不过是三个基本逻辑运算(AND，OR和NOT)的定义
尔代数的公理或假设
的运算的结果。
Axiom 1: 0.0 = 0 Axiom 6: 0+1 = 1
Axiom 2: 0.1 = 0 Axiom 7: 1+0 = 1
Axiom 3: 1.0 = 0 Axiom 8: 1+1 = 1
Axiom 4: 1.1 = 1 Axiom 9: 0 = 1
Axiom 5: 0+0 = 0 Axiom 10: 1 = 0
Bad on the axioms we can conclude many laws of Boolean Algebra which are listed below,
根据这些公理，我们可以得出以下布尔代数的许多定律，
Commutative Laws
交换律
A+B = B+A, and
化妆品生产日期A.B =
B.A
什么是浮游生物Associative Laws
关联法
项目自查报告
(A+B) + C = A+(B+C)
(A.B). C = A. (B.C)
AND Laws
与法律
A.A = A
A.A = 0
OR Laws
或法律
A+0 = A
A+1 = 1
A+A = A
A+A = 0
Complementation Laws
补充法
If A = 0 then A = 1
If A = 1 then A = 0
A= A
Distributive Laws
分配法
A(B+C) = AB + AC
A + BC = (A+B). (A+C)催化氧化
Idempotence Law
幂等法
A.A = A, If A=1, then A.A = 1.1 =1 = A and if A=0, then A.A = 0.0 = 0 = A蓝莓功效
A+A = A, If A=1, then A+A = 1+1 =1 = A and if A=0, then A+A = 0+0 = 0 = A
Absorption Law
吸收定律
A + A.
B = A
A.(A+B) = A
De-Morgan's Law
德摩根定律
Connsus Theorem
共识定理
A) AB + A C + BC = AB + A C
Proof:
证明：
LHS = AB + A C + BC
= AB + A C + BC (A+A)
= AB + A C + ABC + ABC
= AB (1+C) + A C (1+C)
= AB + A C = RHS
B) (A+B) (A + C) (B+C) = (A+B) (A + C)
Proof:
证明：
LHS = (A+B) (A + C) (B+C)
= (AA + AC + BA + BC) (B+C)
= (AC + BA + BC) (B+C)
= ABC + ACC + BAB + BAC + BCB + BCC
= ABC + AC + BA + BAC + BC + BC
= ABC + AC + BA + BAC + BC
= AC(B+1) + BA (1+C) + BC
= AC + BA + BC ............. (Equation 1)
RHS = (A+B) (A + C)
= AA + AC + BA + BC
= AC + BA + BC ............. (Equation 2)
Since, Equation 1 = Equation 2
Connsus Theorem is verified.
Equation 1 = Equation 2, Hence Connsus Theorem
共识定理 。
由于等式1 =等式2
等式1 =等式2 ，因此验证了共识定理
布尔代数定律
