
Database System Concepts
7th Edition
ISBN: 9780078022159
Author: Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher: McGraw-Hill Education
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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)
Expert Solution

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Step 1
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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