{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

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

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

This preview shows pages 1–4. Sign up to view the full content.

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

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
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
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

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 6

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

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online