Chapter 03 - Boolean Algebra II-2x2(1)

Chapter 03 - Boolean Algebra II-2x2(1) - Distributive Laws...

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CHAPTER # BOOLEAN ALGEBRA ± II 0QNHP YMJ RTZXJ YT RT[J YT YMJ SJ]Y UFLJ± :XJ YMJ 280 PJ^ YT J]NY YMNX HMFUYJW± ±²³ Multiplying Out and +actoring *xpressions ±²´ *xclusiveµOR and *quivalence Operations ±²± The (onsensus Theorem ±²¶ &lgebraic Simplification of Switching *xpressions ±²· Proving the Validity of an *quation /istributive 5aws ,iven an expression in productµofµsums form¸ the corresponding sumµofµproducts expression can be obtained by multiplying out¸ using the two distributive laws¹ X º Y ± Z » " XY ¼ XZ º±µ³» º X ± Y »º X ± Z » " X ± YZ º±µ´» .n addition¸ the following theorem is very useful for factoring and multiplying out¹ º X ± Y »º X′ ± Z » " XZ ± X ƍ Y º±µ±» 2]FRUQJ ²³´µ¶· U± ¸³ .n the following example¸ if we were to multiply out by brute force¸ we would generate ³½´ terms¸ and ³·¾ of these terms would then have to be eliminated to simplify the expression² .nstead¸ we will use the distributive laws to simplify the process² The same theorems that are useful for multiplying out expressions are useful for factoring² 'y repeatedly applying º±µ³»¸ º±µ´»¸ and º±µ±»¸ any expression can be converted to a productµofµsums form²
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0xclusive±8; and 0quivalence 8perations The exclusive-OR operation ± ² is defined as follows³ The equivalence operation ± ² is defined by³ Section 3±2² p± 64 We will use the following symbol for an exclusive± 8; gate³ The following theorems apply to exclusive OR³ Section 3±2² p± 65 We will use the following symbol for an equivalence gate³
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Section 3±2² p± 66 'ecause equivalence is the complement of exclusive±8; ± an alternate symbol of the equivalence gate is an exclusive±8; gate with a complemented output² The equivalence gate is also called an exclusive±78; gate³ *xample ´² *xample µ² <ection ²³´ µp³ ¶¶· 'y ¶·¸¹º and ¶·¸´»º± F " [¶ A′B º
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Chapter 03 - Boolean Algebra II-2x2(1) - Distributive Laws...

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