The Boolean SOP expression obtained from the truth table is:

Inputs			Output
A	B	C	X
0	0	0	0
0	0	1	1
0	1	0	0
0	1	1	0
1	0	0	0
1	0	1	0
1	1	0	1
1	1	1	0

Concept:

We can minimize the Boolean expression/truth table of ‘n’ variable using a K-map in which 2ⁿ cells are present.

Steps to solve expression using K-map:

• Select the K-map according to the number of variables (Cells = 2ⁿ)
• Identify maxterm or minterm as given as per the problem.
• For SOP, put 1’s in blocks of K-map respective to the minterms.
• For POS, put 0’s in blocks of K-map respective to the max terms.
• To minimize, make rectangular groups containing total terms in power of two (like 1, 2, 4, 8..).
• From the groups made in step-5, find the product terms & add them for SOP form.

Calculation:

The truth table given is:

The 3 – variable K-map corresponding to the given truth table is drawn with 2³ = 8 (cells) as shown:

By making a group of 1’s,

Output (X) = A̅ B̅ C + A B C̅ 

Short Trick:

The output expression is simply the SOP representation of inputs that gives an output of 1 (HIGH).

From the given Truth Table, the output is 1 for A = 0, B = 0, C = 1, i.e. (A̅B̅C)

and the output is 1 for inputs A = 1, B = 1, C = 0, i.e. (ABC̅)

So, X = A̅B̅C + ABC̅