Solutions For Digital Design Chapter 2 Problem 2PE

Step-by-Step Solution

Solution 1

Consider the following Boolean expression:

$$ F=x^{\prime} y^{\prime} z $$

Observe that there are three variables \(x, y\), and \(z\), hence three variable truth table is required.

Design a truth table for the expression, with F as output.

The following table shows the truth table of the function, .

Picture 1

Note that the function \(F\) is high only when \(x=0, y=0\), and \(z=1\), because the function is AND operation of negation of \(x\), negation of \(y\) with \(z\) that is, \(F=x^{\prime} y^{\prime} z\).

Therefore, the truth table for the Boolean expression is shown in Table 1 .

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