Morris Mano Edition 3 Exercise 2 Question 14 (Page No. 71)

Question

Convert the following to the other canonical Form

$(a) F(A,B,C,D) = \prod(0,1,2,3,4,6,12)$

$(b) F(x,y,z)  = \sum(1,3,7)$

Answer 1

$(a) F(A,B,C,D) = \prod(0,1,2,3,4,6,12)$

Canonical Product of Sum$:$
${\color{Red} {F(A,B,C,D)=(A+B+C+D)\cdot(A+B+C+\overline{D})\cdot(A+B+\overline{C}+D)\cdot(A+B+\overline{C}+\overline{D})}}$

${\color{Red}{\cdot(A+\overline{B}+C+D)\cdot(A+\overline{B}+C+\overline{D})\cdot(\overline{A}+\overline{B}+C+D)}}$

 we can write like this also $F(A,B,C,D) = \sum(5,7,8,9,10,11,13,14,15)$

Canonical Sum of Product$:$

$F(A,B,C,D)=\overline{A}B\overline{C}D+\overline{A}BCD+A\cdot\overline{B}\cdot\overline{C}\cdot\overline{D}+A\overline{B}\cdot\overline{C}D+A\overline{B}C\overline{D}+A\overline{B}CD+AB\overline{C}D+ABC\overline{D}+ABCD$

$(b) F(x,y,z)  = \sum(1,3,7)$

Canonical Sum of Product$:$

${\color{Magenta}{F(x,y,z)=\overline{x}\cdot\overline{y}\cdot z+\overline{x}\cdot y\cdot z+x\cdot y\cdot z} }$

 we can write like this $F(x,y,z)=\prod(0,2,4,5,6)$

Canonical Product of Sum$:$

$F(x,y,z)=(x+y+z)\cdot(x+\overline{y}+z)\cdot (\overline{x}+y+z)\cdot (\overline{x}+y+\overline{z})\cdot (\overline{x}+\overline{y}+z)$

Comments

it is asking for canonical fome??

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Ok , thanks for correcting me i will add it.

Answer 2

 canonical Form:  Boolean function will contain all the variables in either true form or complemented form is called canonical form.

• In Minterm, we look for the functions where the output results in “1” while in Maxterm we look for function where the output results in “0”.