# JEE Main & Advanced Physics Semiconducting Devices Boolean Algebra

Boolean Algebra

Category : JEE Main & Advanced

(1) In Boolean algebra only two states of variables (0 and 1) are allowed.

(2) The variables (A, B, C ....) of Boolean Algebra are subjected to three operations.

(i) OR Operation : Represented by (+) sign

Boolean expression  $Y=A+B$

When switch A or B is closed ? Bulb glows

(ii) AND Operation : Represented by $(.)$ sign

Boolean expression $Y=A\cdot B$

When switches A and B both are closed ? Bulb glows

(iii) NOT Operation : Represented by bar over the variables

Boolean expression  $Y=\bar{A}$

(3) Basic Boolean postulates and laws

(i) Boolean Postulates : $0+A=A,$          $1\,\,\cdot \text{ }A=A,$

$1+A=1,$

$0\cdot A=0,$

$A+\bar{A}=1$

(ii) Identity law :               $A+A=A,$         $A\cdot A=A$

(iii) Negation law :            $\overline{{\bar{A}}}=A$

(iv) Commutative law : $A+B=B+A,$    $A\cdot B=B\cdot A$

(v) Associative law :        $(A+B)+C=A+(B+C),$

$(A\cdot B)\cdot C=A\cdot (B\cdot C)$

(vi) Distributive law :       $A\cdot (B+C)=A\cdot B+A\cdot C$

$(A+B)\cdot (A+C)=A+BC$

(vii) Absorption laws :    $A+A\cdot B=A,$          $A\cdot (A+B)=A$

$\overline{A}\,\text{ }\!\!\cdot\!\!\text{ }\,(A+B\text{)}=\overline{A}\,\text{ }\!\!\cdot\!\!\text{ }\,B$

(viii) Boolean identities :   $A+\overline{A}\,B=A+B$, $A(\overline{A}+B)=AB$,

$A+BC=(A+B)\,(A+C)$, $(\overline{A}+B)\,\text{ }\!\!\cdot\!\!\text{ }\,\text{(}A+C)\,=\overline{A}C+AB$

(ix) De Morgan's theorem : It states that the complement of the whole sum is equal to the product of individual complements and vice versa i.e.

$\overline{A+B}=\bar{A}\cdot \bar{B}$ and $\overline{A\cdot B}=\bar{A}+\bar{B}$

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