POS BOOLEAN EXPRESSION FROM TRUTH TABLE

POS BOOLEAN EXPRESSION FROM TRUTH TABLE - Here you would learn how to write Boolean Expression in POS (Product of Sum) form from Truth Table Step by Step with the help of example.

POS BOOLEAN EXPRESSION FROM TRUTH TABLE

Let us take an example:

Convert the given truth table into Boolean expression in Product of Sum (POS) form:

A	B	C	Y
0	0	0	1
0	0	1	0
0	1	0	1
0	1	1	0
1	0	0	1
1	0	1	1
1	1	0	0
1	1	1	1

Step 1: Form maxterms (or sum terms) from the input combination for which output (Y) is equal to 0.

For a maxterm, a variable in complemented form is considered as 1 (for example A^/=1) and its uncomplemented form is considered as 0 (i.e., A=0)

Here, for the input combinations 001, 011 and 110 of ABC the output Y is 0.

The corresponding maxterms would be:

ABC	Maxterm
001	A+B+C^/
011	A+B^/+C^/
110	A^/+B^/+C

Step 2: Use logical AND operators (i.e., ‘.’) between all the maxterms to get the expression in standard or canonical Product of Sum (POS) form.

i.e., Y = (A+B+C^/) . (A+B^/+C^/) . (A^/+B^/+C)

In this way a standardor or canonical POS Boolean expression can be formed from a truth table. To simplify the standard POS expression you need the help of Boolean Theorems or Karnaugh Map.

This article would definitely help you to clear your concepts in finding "POS BOOLEAN EXPRESSION FROM TRUTH TABLE"

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