Boolean Function

BOOLEAN FUNCTION

What are Boolean Functions?

In Boolean algebra, we deal with various logic operations and binary variables. Here, we make use of an algebraic expression known as the Boolean Expression to describe the Boolean Function. The Boolean Expression contains the logic operation symbols, binary variables, and the constants 1 and 0. Let us now consider the example given below:

F (W, X, Y, Z) = W + XȲ + WZY Equation No. 1

The left side of this equation here represents the output B. So we can state equation no. 1

B = W + XȲ + WZY

Truth Table Formation

We use a truth table to represent a table that has all the combinations of inputs along with their corresponding results. Conversion of the switching equation to the truth table is also possible. For instance, let us consider the switching equation given as follows:

F (W, X, Y) = W + XY

The output here would be high (1) when W = 1 or XY = 1 or when both of these are 1. For this equation, we get the truth table by Table (a). The total number of rows present in the truth table would be 2n, where n refers to the total number of input variables (for the given equation, n=3). Hence, there are a total of 23 = 8 possible input combinations.