《计算机专业英语》电子教案–第3章.ppt

Computer English Chapter 3 Number Systems and Boolean Algebra For any given element of a Boolean algebra, there is a unique complement a with the property that a+a=1 and aa=0. Boolean addition and multiplication are associative and commutative, as are ordinary addition and multiplication, but otherwise have somewhat different properties. The principal properties are given in Table 3-2, where a, b, and c are any elements of a Boolean algebra. 3.2 Boolean Algebra 对于一个布尔代数中任意给定元素a，都有一个唯一的补a?，它满足a+a?=1和aa?=0。布尔加和布尔乘与普通的加和乘一样，满足结合律和交换律，但除此之外含有一些不太相同的特性。其主要特性由表3-2给出，其中a, b和c是一个布尔代数中的任意元素。 3.2 Boolean Algebra Table 3-2 (a+b)=ab (ab)=a+b DeMorgan’s laws德?摩根定理 a+ab=a a(a+b)=a Absorption laws 吸收律 a+a=a aa=a Idempotency 同一律 a(b+c)=ab+ac a+(bc)=(a+b)(a+c) Distributivity 分配律 Since a finite set of n elements has exactly 2n subsets, and it can be shown that the finite Boolean algebras are precisely the finite set algebras, each finite Boolean algebra consists of exactly 2n elements for some integer n. For example, the set algebra for the set T defined above corresponds to a Boolean algebra of 32 elements. 3.2 Boolean Algebra 由于n个元素的有限集有且只有2n个子集，而且很显然有限布尔代数一定是有限集合代数，所以对某个整数n而言，每个有限布尔代数也有且只有2n个元素。例如，上文定义的集合T的集合代数就对应一个有32个元素的布尔代数。 While it is possible to use a different symbol to denote each element of a Boolean algebra, it is often more useful to represent the 2n elements of a finite Boolean algebra by binary vectors having n components. With such a representation the operations of the Boolean algebra are accomplished componentwise by considering each component as an independent two-element Boolean algebra. This corresponds to representing subsets of a finite set by binary vectors. 3.2 Boolean Algebra 虽然我们可以用不同的符号来表示布尔代数中的每一个元素，但最常用的方法是用一个有n个分量的二进制向量来表示一个有限布尔代数的2n个元素。用这样一种表示方法，布尔代数的所有运算都以分量的形式完成，而每一个分量被认为是一个独立的二值布尔代数。这种做法对应于用二进制向量来表示一个有限集的子集。 For example, since the set T has five elements, we may represent its subsets by five-component binary vectors, eac