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Q.1. Using algebraic manipulation, simplify the following expressions to minimum number of literals and express the simplified function as SOP (sum of products i.e. AND terms that are ORed) and POS (product of sums i.e. OR terms that are ANDed): (i) F(A,B,C) = A'B'C' + A'BC + A'B'C + ABC (1) F(A,B,C) = (A+B+C) (A'+B'+C') (A+B'+C') (A+B+C') (ii) F(A,B,C,D) =A'B'D + A'D + BC (A' + D') (should be simplified to 5 literals only) (iii) F(A,B,C,D) = (A+B+C+D')•(A+B+C²+D')•(A+B²+C+D') (A+B'+C'+D') Hint: To convert a single product term to POS terms, OR with one of the variables in the term ANDed with its complement (e.g. AA', BB', CC' or DD'). This amounts to ORing with 0 which does not affect he expression).

Q.1. Using algebraic manipulation, simplify the following expressions to minimum number of literals and express the simplified function as SOP (sum of products i.e. AND terms that are ORed) and POS (product of sums i.e. OR terms that are ANDed): (i) F(A,B,C) = A'B'C' + A'BC + A'B'C + ABC (1) F(A,B,C) = (A+B+C) (A'+B'+C') (A+B'+C') (A+B+C') (ii) F(A,B,C,D) =A'B'D + A'D + BC (A' + D') (should be simplified to 5 literals only) (iii) F(A,B,C,D) = (A+B+C+D')•(A+B+C²+D')•(A+B²+C+D') (A+B'+C'+D') Hint: To convert a single product term to POS terms, OR with one of the variables in the term ANDed with its complement (e.g. AA', BB', CC' or DD'). This amounts to ORing with 0 which does not affect he expression).

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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Q.1. Using algebraic manipulation, simplify the following expressions to minimum number of literals and express the simplified function as SOP (sum of products i.e. AND terms that are ORed) and POS (product of sums i.e. OR terms that are ANDed): (i) F(A,B,C) = A'B'C' + A'BC + A'B'C + ABC (1) F(A,B,C) = (A+B+C) (A'+B'+C') (A+B'+C') (A+B+C') (ii) F(A,B,C,D) =A'B'D + A'D + BC (A' + D') (should be simplified to 5 literals only) (iii) F(A,B,C,D) = (A+B+C+D') (A+B+C'+D')•(A+B'+C+D')•(A+B'+C'+D') Hint: To convert a single product term to POS terms, OR with one of the variables in the term ANDed with its complement (e.g. AA', BB', CC' or DD'). This amounts to ORing with 0 which does not affect the expression). T
Transcribed Image Text:Q.1. Using algebraic manipulation, simplify the following expressions to minimum number of literals and express the simplified function as SOP (sum of products i.e. AND terms that are ORed) and POS (product of sums i.e. OR terms that are ANDed): (i) F(A,B,C) = A'B'C' + A'BC + A'B'C + ABC (1) F(A,B,C) = (A+B+C) (A'+B'+C') (A+B'+C') (A+B+C') (ii) F(A,B,C,D) =A'B'D + A'D + BC (A' + D') (should be simplified to 5 literals only) (iii) F(A,B,C,D) = (A+B+C+D') (A+B+C'+D')•(A+B'+C+D')•(A+B'+C'+D') Hint: To convert a single product term to POS terms, OR with one of the variables in the term ANDed with its complement (e.g. AA', BB', CC' or DD'). This amounts to ORing with 0 which does not affect the expression). T
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