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Chapter 12: Q18E (page 828)

Construct a half adder using NOR gates.A multiplexer is a switching circuit that produces as output one of a set of input bits based on the value of control bits.

Short Answer

Expert verified

The circuit is

Step by step solution

01

Defining of gates

There are three types of gates.

It is also called NOT gate.

02

construct a circuit.

The circuit is

Therefore, this is the required results.

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Most popular questions from this chapter

Suppose that \(F\) is a Boolean function represented by a Boolean expression in the variables\({x_1}, \ldots ,{x_n}\). Show that \({F^d}\left( {{x_1},{x_2}, \ldots ,{x_n}} \right) = \overline {F\left( {{{\bar x}_1},{{\bar x}_2}, \ldots ,{{\bar x}_n}} \right)} \)

How many cells in a \({\bf{K}}\)-map for Boolean functions with six variables are needed to represent \({{\bf{x}}_{\bf{1}}}{\bf{,}}{{\bf{\bar x}}_{\bf{1}}}{{\bf{x}}_{\bf{6}}}{\bf{, }}{{\bf{\bar x}}_{\bf{1}}}{{\bf{x}}_{\bf{2}}}{{\bf{\bar x}}_{\bf{6}}}{\bf{,}}{{\bf{x}}_{\bf{2}}}{{\bf{x}}_{\bf{3}}}{{\bf{x}}_{\bf{4}}}{{\bf{x}}_{\bf{5}}}\), and \({{\bf{x}}_{\bf{1}}}{{\bf{\bar x}}_{\bf{2}}}{{\bf{x}}_{\bf{4}}}{{\bf{\bar x}}_{\bf{5}}}\), respectively\({\bf{?}}\)

In Exercises 35–42,Use the laws in Definition \(1\) to show that the stated properties hold in every Boolean algebra.

Show that in a Boolean algebra, if \(x \vee y{\bf{ = }}0\), then \(x{\bf{ = }}0\) and \(y{\bf{ = }}0\), and that if \(x \wedge y{\bf{ = }}1\), then \(x{\bf{ = }}1\) and \(y{\bf{ = }}1\).

Show that \({\bf{x\bar y + y\bar z + \bar xz = \bar xy + \bar yz + x\bar z}}\).

Show that the set of operators \(\left\{ {{\bf{ + , \cdot}}} \right\}\) is not functionally complete.
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