電氣工程及其自動化專業(yè)英語第二章課文翻譯-資料下載頁
2025-04-07 00:48本頁面
【正文】 對于“與”有AB＝BA，而對于“或”有A＋B＝B＋A。這個法則表明了可以如上式所示進行運算的組合和展開Before we show the remaining rules of Boolean algebra for digital devices, let us confirm the distributive rule for AND by writing the truth table, Table 2l. We will discover soon how we knew that we could write AB + C = (A + C)(B + C), which is proved by the truth table to be a proper expansion. 在我們展示數(shù)字設(shè)備布爾代數(shù)的剩下的那個法則之前，讓我們通過寫出真值表的方式即真值表2－1來驗證對于“與”的分配律。我們將很快發(fā)現(xiàn)如何寫出等式AB＋C＝（A＋C）（B＋C），這一等式由真值表證明了是一個正確的展開式。The more plex expression and its simpler form yield identical values. Because binary logic is dominated by an algebra in which a sum of ones equals one, the truth table permits us to identify the equivalence among algebraic expressions. A truth table may be used to find a simpler equivalent to a more plex relation among variables, if such an equivalent exists. We will see shortly how the reduction of plexity may be achieved in a systematic manner with truth tables and other techniques更為復(fù)雜的表達式和它的一次式產(chǎn)生了相等的值。由于二進制邏輯取決于某一代數(shù)，其單個變量之和等于一個變量，所以真值表允許我們在代數(shù)表達式中找出等效值，我們可以使用真值表來求出一個等效于變量之間較復(fù)雜的關(guān)系式的一次表達式。如果這樣的等效關(guān)系存在，我們將很快看到利用真值表以及其它方法以一種系統(tǒng)性的方式如何完成這樣一個復(fù)雜步驟的簡化工作。Some additional relations in the algebra, which use identity and null, are worth nothing. Here we illustrate properties of the AND and OR operations that use the distributive rules and the fact that I is always l and null is always 0.AND AI = A or A1 = AOR A+ null = A A + 0 = AAND A = null A = 0OR A + = I A + =1 AND A null = null A0 = 0OR A + I = I A + 1 = 1AND AA = AOR A + A = A The relation points out an important fact, that is, that I, the identity, is the universal set. Null is called the empty ，這些式子中使用單位一和零，是沒有意義的，這里我們列舉了運用分配律后“與”和“或”運算的性質(zhì)，結(jié)果是1永遠(yuǎn)是1而零永遠(yuǎn)是0。與：AI＝A即A1＝A或：A＋null＝A即A＋0＝A與： 即或： 即 與：Anull＝0即A0＝0或：A＋I＝I即A＋1＝1與：AA＝A或：A＋A＝A關(guān)系式A＋A＝I指出了一個重要事實，即I，也就是單位量，是全集，而零被稱為空集。We have considered several logical relations. For the twovalue Boolean algebra of digital electronics, the choice of the technique depends upon the nature of the function whose reduction is desired. Some simple functions may be easily reduced by examining their truth table。 others require the manipulation of Boolean algebra to reveal the relationship . When we consider the circuit foradding binary numbers, we see that Boolean algebra is required to discover a simplification in that particular application我們已經(jīng)研究了幾種邏輯關(guān)系。對于電子學(xué)的二值布爾代數(shù)來說，選擇何種方法取決于我們所期望的簡化函數(shù)的性質(zhì)。一些簡單的函數(shù)可以通過觀察它們的真值表很容易進行簡化；而另一些函數(shù)需要通過計算布爾代數(shù)來揭示它們的關(guān)系。當(dāng)我們研究有關(guān)二進制數(shù)相加的電路時，我們將看到需要布爾代數(shù)來揭示該特定應(yīng)用中的簡化過程5
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