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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

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

Use a \({\bf{3 - }}\)cube \({{\bf{Q}}_{\bf{3}}}\) to represent each of the Boolean functions in Exercise \(5\) by displaying a black circle at each vertex that corresponds to a \({\bf{3 - }}\)tuple where this function has the value \({\bf{1}}\).

Explain how to construct the sum-of-products expansion of a Boolean function.

Construct a \({\bf{K}}\)-map for \({\bf{F(x,y,z) = xz + yz + xy\bar z}}\). Use this \({\bf{K}}\)-map to find the implicants, prime implicants, and essential prime implicants of \({\bf{F(x,y,z)}}\).

Use the Quine–McCluskey method to simplify the sum-of-products expansions in Example \(4\).
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