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Chapter 12: Q17E (page 828)

Construct a half adder using NAND gates.

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 result.

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Most popular questions from this chapter

Show that the relation \( \le \) is a partial ordering on the set of Boolean functions of degree \(n\).

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 \(y{\bf{ = }}1\).

Construct a circuit that compares the two-bit integers\({{\bf{(}}{{\bf{x}}_{\bf{1}}}{{\bf{x}}_{\bf{o}}}{\bf{)}}_{\bf{2}}}\)and\({{\bf{(}}{{\bf{y}}_{\bf{1}}}{{\bf{y}}_{\bf{o}}}{\bf{)}}_{\bf{2}}}\), returning an output of 1 when the first of these numbers is larger and an output of 0 otherwise.

Simplify these expressions.

\(\begin{array}{l}{\bf{a) x}} \oplus {\bf{0}}\\{\bf{b) x}} \oplus {\bf{1}}\\{\bf{c) x}} \oplus {\bf{x}}\\{\bf{d) x}} \oplus {\bf{\bar x}}\end{array}\)

Is there a single type of logic gate that can be used to build all circuits that can be built using \({\bf{OR}}\)gates, \({\bf{AND}}\) gates, and inverters?
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