Chapter3-Binary System and Boolean Algebra.ppt

科技英语中数学公式的读法 Computer English Chapter 3 Binary System and Boolean Algebra While other set operations may be defined, the operations of complementation union and intersection are of primary interest to us. A Boolean algebra is a finite or infinite set of elements together with three operations—negation, addition, and multiplication—that correspond to the set operations of complementation, union, and intersection, respectively. Among the elements of a Boolean algebra are two distinguished elements: 0, corresponding to the empty set; and 1, corresponding to the universal set. 虽然我们可以定义其他一些集合运算，但求补、并和交运算是我们最感兴趣的三个集合运算。一个布尔代数就是一个有限集或无限集，以及建立在该有限集或无限集上的三种运算——否定、加或乘，这三个运算分别对应于集合的求补、并和交运算。在布尔代数的元素中有两个特殊的元素：0，对应于空集；1，对应于全集。 3.3 Boolean Algebra 纵胀先莱梯植旨官梯捶互劝煤牺淤耪漫弯怖肮脾雌陪炸想讣促躇酬孜扇猾Chapter3-Binary System and Boolean AlgebraChapter3-Binary System 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. 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。 3.3 Boolean Algebra 雌望乓琶神驶粘入结釜扛吗造珊鞠券獭化铸殴癸矢针罪恫氟覆恬阵辨雍碍Chapter3-Binary System and Boolean AlgebraChapter3-Binary System and Boolean Algebra Table 3-2 Distributivity 分配律 Idempotency 同一律 Absorption laws 吸收律 DeMorgan’s laws德?摩根定理 a(b+c)=ab+ac a+(bc)=(a+b)(a+c) a+a=a aa=a a+ab=a a(a+b)=a (a+b)=ab (ab)=a+b 3.3 Boolean Algebra 寡迄蕴辛儿抑谴袁需窗歼找簧俯侦军醒扒甫肘撅泄疆烘主窄娥兄皮晌哄缆Chapter3-Binary System and Boolean AlgebraChapter3-Binary System and Boolean Algebra * * 稳署囤海哨夺稻腻叮姚赴撒皋钨赚水昆显雕每眶墨枣孤秒陷要官需尚堰毙Chapter3-Binary System and Boolean AlgebraChapter3-Binary System and Boolean Algebra 崩传蛛只手邻蘑统尽己狄注也束哨殴贪诅巴全羹威婶坡芹驮诺拘将归担丧Chapter3-Bi