IGNOU MTE 13 2018 - Make a table of the values of the Boolean functionf (x1;x2;x3) = x2

Question

Make a table of the values of the Boolean function
f (x₁;x₂;x₃) = x₂ $\bigoplus$ (x₁ $\wedge$ x₃)
Write the function in DNF using the table.

14 Feb 2018

Answer :

Word Count : 313

To solve the Boolean function numerically and create a table for the function: The Boolean function is: \[ f(x_1, x_2, x_3) = x_2 \oplus (x_1 \wedge x_3) \] Where: - $\oplus$ represents the XOR (exclusive OR) operation. - $\wedge$ represents the AND operation. ### Step 1: Create the Truth Table We'll list all the combinations of values for $x_1$, $x_2$, and $x_3$, and compute the value of $f(x_1, x_2, x_3)$ for each combination. | $x_1$ | $x_2$ | $x_3$ | $x_1 \wedge x_3$ | $x_2 \oplus (x_1 \wedge x_3)$ | |:------:|:------:|:------:|:------------------:|:--------------------------------:| | 0 | 0 | 0 | 0 | 0 | | 0 | 0 | 1 | 0 | 0 |

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