Question

Find the values of these expressions.

\(\begin{array}{c}{\bf{a)1}} \cdot {\bf{\bar 0}}\\{\bf{b)1 + \bar 1}}\\{\bf{c)\bar 0}} \cdot {\bf{0}}\\{\bf{d)}}\overline {{\bf{(1 + 0)}}} \end{array}\)

Short answer

(a) The value of the given expression \({\bf{1}} \cdot {\bf{\bar 0}}\) is 1

(b) The value of the given expression \({\bf{1 + \bar 1}}\) is 1

(c) The value of the given expression \(\bar 0 \cdot 0\) is 0

(d) The value of the given expression \(\overline {{\bf{(1 + 0)}}} \) is 0

Step-by-step solution

Definition

The complement of an element: \({\bf{\bar 0 = 1}}\) and \({\bf{\bar 1 = }}0\)

The Boolean sum + or\(OR\)is 1 if either term is 1.

The Boolean product \( \cdot \) or \(AND\) is 1 if both terms are 1.

(a) Using the Boolean product

Since both terms are 1 in the Boolean product.

Therefore, the answer is 1.

(b) Using the Boolean sum

Since one of the terms is 1 in the Boolean sum.

Therefore, the answer is 1.

(c) Using the Boolean product

\(\begin{array}{c}\bar 0 \cdot 0{\bf{ = }}1 \cdot 0\\{\bf{ = }}0\end{array}\)

Since one of the terms is 0 in the Boolean product.

Therefore, the answer is 0.

(d) Using the Boolean sum

\(\begin{array}{c}\overline {{\bf{(1 + 0)}}} {\bf{ = \bar 1}}\\{\bf{ = 0}}\end{array}\)

Since one of the terms is 1 in the Boolean sum.

Therefore, the answer is 0.