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Given: F(a,b.c.d)=(a+b+c'+d')(a'+b'+c')(a+b+d)(a'tc) (a) Express F as a minterm expansion. (use m-notation) (b) Express F as a maxterm expansion. (use M-notation) (c) Express F' as a minterm expansion. (use m-notation) (d) Express F' as a maxterm expansion. (use M-notation) ww wwww

Given: F(a,b.c.d)=(a+b+c'+d')(a'+b'+c')(a+b+d)(a'tc) (a) Express F as a minterm expansion. (use m-notation) (b) Express F as a maxterm expansion. (use M-notation) (c) Express F' as a minterm expansion. (use m-notation) (d) Express F' as a maxterm expansion. (use M-notation) ww wwww

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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Given: F(a,b,c,d)=(a+b+c'+d')(a'+b'+c')(a+b+d)(a'+c) (a) Express F as a minterm expansion. (use m-notation) (b) Express F as a maxterm expansion. (use M-notation) (c) Express F' as a minterm expansion. (use m-notation) (d) Express F' as a maxterm expansion. (use M-notation)
Transcribed Image Text:Given: F(a,b,c,d)=(a+b+c'+d')(a'+b'+c')(a+b+d)(a'+c) (a) Express F as a minterm expansion. (use m-notation) (b) Express F as a maxterm expansion. (use M-notation) (c) Express F' as a minterm expansion. (use m-notation) (d) Express F' as a maxterm expansion. (use M-notation)
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As you have posted multiple parts we will solve the first part for you.

Given F(a,b,c,d)=(a+b+c'+d')(a'+b'+c')(a+b+d)(a'+c)

It is given in the form of product of max terms

We know that complement of max term is min-term, taking complement of max-terms we get

F(a,b,c,d)=a'b'cd+abc+abd+a'c  (by demorgan's law)

              =a'b'cd+abc(d+d')+abd(c+c')+a'c(b+b')(d+d')  expand the terms to include all 4 variables

              =a'b'cd+abcd+abcd'+abcd+abc'd+a'bcd+a'bcd'+a'b'cd+a'b'cd'  removing identical terms (A+A=A)

             =a'b'cd+abcd+abcd'+abc'd+a'bcd+a'bcd'+a'b'cd'

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