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Statement form of Boolean Expression

Same way as the Venn diagram and circuit diagram we can also represent Boolean expression in form statement.

Example 1:

Logic circuits have 3 I/P A, B, and C, and O/P Y, Y is 1 for the following combinations.

i) A and C are true

ii) B and C are false

iii) A, B and C are true

iv) A, B and C are false

Then minimize expression for O/P Y is = ?

Solution:

As per the above statement Boolean Expression of output function is = 

Now we can minimize the Boolean function:

Example 2:

A logic circuit has 3 inputs x, y, and z, and output F, F is 1 when exactly any two inputs are true. 

Solution:

As per the above statement, it is clear that output is 1 when exactly any two inputs are 1.

We can understand it with true table:

So, Boolean Expression when the output F is 1, 

Question:

A logic circuit has 3 inputs x, y, and z, and output F, F is 1 when the majority number of input is 1 (true).

Which one is Boolean Expression as per the above statement:

Solution:

Output F is 1 when the majority number of input is 1 (true).

Truth table as per statement:

So, Boolean Expression of output when the majority of input is 1: 

Now we can minimize the Boolean Expression:

So, option (a) is the correct answer.