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. 

Combinational logic circuit

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

Combinational logic circuit

Block diagram


Combinational logic circuit

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.

Combinational-logic-circuit


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)