Combinational logic circuit

The combinational logic circuit is defined as a combination of logic devices . The output of a Combinational logic circuit is a function o...

The combinational logic circuit is defined as a combination of logic devices. The output of a Combinational logic circuit is a function of present values of input variables and independent of the previous values. 

f(A,B,C)=AB+C

Block diagram

Design with 3 inputs

A, B, C, and the condition are when any output will be low only when A is high while B and C are different.

Solution:

A is high that means A = 1.

B and C are different means  when B =0 then C =1 and when B= 1 then C =0.

Here inputs are 3 . So, combinations = 2³ =8 

A	B	C	x
0	0	0	1
0	0	1	1
0	1	0	1
0	1	1	1
1	0	0	1
1	0	1	0
1	1	0	0
1	1	1	1

Here A = 0 in first 4 entries. So, the value of X will be 1 because it not satisfying the condition A =1 (A is low in this case).

In the next two rows, it is satisfying both of the conditions. A is high (A=1) and B and C are different. That is why we got X =0.

In the final two rows A =1. But the value of B and C are equal. So, these are not fulfilling the conditions.

Equation if inputs are not satisfying the conditions

X = ĀB̄C̄+ĀB̄C+ĀBC̄+ĀBC+ABC̄+ABC

    = ĀB̄(C+C̄)+ĀB(C̄+C)+AB(C̄+C)

    

    = ĀB̄+ĀB+AB [C̄+C=1]

   

    = AB+ĀB̄+ĀB

   

    = (A⊕B)+ĀB

Equation if inputs are satisfying the conditions

X̄= AB̄C+ABC̄

   

   = A(B̄C+BC̄)

   = A(B⊕C)