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1. Convert the following expressions into sum-of-products and product-of-sums forms: (a) (XY+Z)(Y+XZ) (b) (Ā+B)(B+C) (c) WXY+WXZ+WXZ+YZ

1. Convert the following expressions into sum-of-products and product-of-sums forms: (a) (XY+Z)(Y+XZ) (b) (Ā+B)(B+C) (c) WXY+WXZ+WXZ+YZ

Database System Concepts
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
Problem 1PE
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4. Convert the following expressions into sum-of-products and product-of-sums forms: (a) \((XY + Z)(Y + XZ)\) (b) \((\overline{A} + B)(\overline{B} + C)\) (c) \(W\overline{X}Y + WX\overline{Z} + WXZ + Y\overline{Z}\)
Transcribed Image Text:4. Convert the following expressions into sum-of-products and product-of-sums forms: (a) \((XY + Z)(Y + XZ)\) (b) \((\overline{A} + B)(\overline{B} + C)\) (c) \(W\overline{X}Y + WX\overline{Z} + WXZ + Y\overline{Z}\)
Expert Solution
Step 1

a) (XY + Z) (Y + XZ)

= XYY + XXYZ + YZ + XZZ

= XY + XYZ + YZ + XZ

Sum of product

 = XY ( Z + Z' ) + XYZ + (X + X' )YZ + X ( Y + Y' )Z

= XYZ + XYZ' + XYZ + XYZ + X'YZ + XYZ + XY'Z

= XYZ + XYZ' + X'YZ + XY'Z

Product of sum

=(X' + Y' + Z') . (X' + Y' + Z) . (X + Y' + Z') . (X' + Y + Z')

 

 

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