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Q18E

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Discrete Mathematics and its Applications
Found in: Page 828
Discrete Mathematics and its Applications

Discrete Mathematics and its Applications

Book edition 7th
Author(s) Kenneth H. Rosen
Pages 808 pages
ISBN 9780073383095

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Short Answer

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.

The circuit is

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :
TABLE OF CONTENTS

Step 1: Defining of gates

There are three types of gates.

It is also called NOT gate.

Step 2: construct a circuit.

The circuit is

Therefore, this is the required results.

Most popular questions for Math Textbooks

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.
  1. Show that \({\bf{(\bar 1}} \cdot {\bf{\bar 0) + (1}} \cdot {\bf{\bar 0) = 1}}\).
  2. Translate the equation in part (a) into a propositional equivalence by changing each \(0\) into an \({\bf{F}}\), each \(1\) into a \({\bf{T}}\), each Boolean sum into a disjunction, each Boolean product into a conjunction, each complementation into a negation, and the equals sign into a propositional equivalence sign.

Use NAND gates to construct circuits with these outputs.

\(\begin{array}{l}{\bf{a)}}\overline {\bf{x}} \\{\bf{b)x + y}}\\{\bf{c)xy}}\\{\bf{d)x}} \oplus {\bf{y}}\end{array}\)

Construct a circuit that computes the product of the two-bitintegers \({{\bf{(}}{{\bf{x}}_{\bf{1}}}{{\bf{x}}_{\bf{o}}}{\bf{)}}_{\bf{2}}}\)and\({{\bf{(}}{{\bf{y}}_{\bf{1}}}{{\bf{y}}_{\bf{o}}}{\bf{)}}_{\bf{2}}}\).The circuit should have four output bits for the bits in the product. Two gates that are often used in circuits are NAND and NOR gates. When NAND or NOR gates are used to represent circuits, no other types of gates are needed. The notation for these gates is as follows:

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