$A, B$ and $C$ represents switches in 'on' position and $A^{'}, B^{'}$ and $C^{'}$ represent them in 'off' position. Construct a switching circuit representing the polynomial $A B C + A B^{'} C + A^{'} B^{'} C$ . Using Boolean Algebra, prove that the given polynomial can be simplified to $C (A + B^{'})$ . Construct an equivalent switching circuit.

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Solution

The switching circuit representing the given polynomial is as (1) :
Given circuit is
$A B C + A B^{'} C + A^{'} B^{'} C$
$\Rightarrow A C (B + B^{'}) + A^{'} B^{'} C$
$\Rightarrow A C + A^{'} B^{'} C$ [Using $p + p^{'} = 1$ ]
$\Rightarrow C (A + A^{'} B^{'})$
$\Rightarrow C (A + A^{'} B^{'})$ [(Using $(p + q r) = (p + q) (p + r))$ ]
$\Rightarrow C (A + B^{'})$ [Using $p + p^{'} = 1$ ]
Hence, the equivalent simplified circuit is (2)

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Similar questions

P, Q

and

R

represent switches in on position and

P^{'}, Q^{'}

and

R^{'}

represent switches in off position. Construct a switching circuit representing the polynomial

P R + Q (Q^{'} + R) (P + Q R)

. Using Boolean Algebra, simplify the polynomial expression and construct the simplified circuit

Q. Which of the following represents a circuit diagram for the given circuit? Here switch ‘a’ is ON and switch ‘b’ is OFF.

Q. Draw the symbols to represent the following components of electric circuits: Cell, bulb, switch in the ‘ON’ position, switch in the ‘OFF’ position, and battery.

Q. Construct a circuit diagram for the following Boolean Function

(B C + A) (A^{'} B^{'} + C^{'}) + A^{'} B^{'} C^{'}

Using laws of Boolean Algebra, simplify the function and draw the simplified circuit.

Question 1
Draw the symbols to represent the following components of electrical circuits:
Cell, bulb, switch in the ‘ON’ position, switch in the ‘OFF’ position and battery.

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The switching circuit representing the given polynomial is as (1) :Given circuit isABC+AB′C+A′B′C⇒AC(B+B′)+A′B′C⇒AC+A′B′C [Using p+p′=1]⇒C(A+A′B′)⇒C(A+A′B′) [(Using (p+qr)=(p+q)(p+r))]⇒C(A+B′) [Using p+p′=1]Hence, the equivalent simplified circuit is (2)