Let denote logical AND and denote logical OR Consider the

Let * denote logical AND and + denote logical OR. Consider the logic function:

F = (A + B) * (A + C)
Are any of the following logic gate circuits a valid implementation of this function? If so, which circuits?

Solution

F= (A or B) and (A or C)
The truth table for the above function is :

A B C | ( A | B ) & ( A | C )
-------------------------------------------

0 0 0 | 0 0 0 0 0 0 0   
0 0 1 | 0 0 0 0 0 1 1   
0 1 0 | 0 1 1 0 0 0 0   
0 1 1 | 0 1 1 1 0 1 1   
1 0 0 | 1 1 0 1 1 1 0   
1 0 1 | 1 1 0 1 1 1 1   
1 1 0 | 1 1 1 1 1 1 0   
1 1 1 | 1 1 1 1 1 1 1

The circuit option C  has function F= A or (B and C)

The truth table is :

A B C | A | ( B & C )
-------------------------------

0 0 0 | 0 0 0 0 0   
0 0 1 | 0 0 0 0 1   
0 1 0 | 0 0 1 0 0   
0 1 1 | 0 1 1 1 1   
1 0 0 | 1 1 0 0 0   
1 0 1 | 1 1 0 0 1   
1 1 0 | 1 1 1 0 0   
1 1 1 | 1 1 1 1 1

As we can see the circuit C has same truth table as of our function\'s truth table. Hence Option C is the answer.

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