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b) With the help of using Boolean laws; Find the Minterms and Maxterms of the function, F (a,b,c) = a'+bc'. %3D

b) With the help of using Boolean laws; Find the Minterms and Maxterms of the function, F (a,b,c) = a'+bc'. %3D

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
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b) With the help of using Boolean laws; Find the Minterms and Maxterms of the function, F (a,b,c) = a'+bc'. %3D
Transcribed Image Text:b) With the help of using Boolean laws; Find the Minterms and Maxterms of the function, F (a,b,c) = a'+bc'. %3D
Expert Solution
Step 1

Given boolean function

F(a,b,c) = a' + bc'

Finding minterms:

We need to add missing variables by multiplying x+x' = 1 in each term where x is the missing variable.

F(a,b,c) = a'(b + b') + bc'     (apply Complement law, A'+A = 1)

= a'b + a'b' + bc'

= a'b(c +c') + a'b'(c + c') + (a + a')bc'    (apply Complement law, A'+A = 1)

= a'bc + a'bc' + a'b'c + a'b'c' + abc' + a'bc'  (apply Idempotent law, A+A = A)

= a'bc + a'bc' + a'b'c + a'b'c' + abc' 

Rearrange the minterms in ascending sequence

F(a,b,c) = a'b'c' + a'b'c + a'bc' +a'bc + abc'

F(a,b,c) = m0 + m1 +m2 + m3 + m6

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