/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 13 (a) Give the first four digits i... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Problem 13

(a) Give the first four digits in the binary representation of \(\frac{1}{3}\). (b) Give the complete binary representation of \(\frac{1}{3}\).

Short Answer

Expert verified
(a) The first four binary digits of 1/3 are 0.0101. (b) The complete binary representation of 1/3 is 0.0101 recurring.

Step by step solution

01

Part (a): Convert Fraction to Binary

To find the first four binary digits of 1/3, begin by multiplying 1/3 by 2 to get 2/3. The integer part of the result is 0, which is the first binary digit. The fractional part is 2/3.\n Multiply 2/3 by 2 to get 4/3. The integer part of this result is 1, which is the second binary digit. The fractional part is 1/3.\n The process repeats again: multiply 1/3 by 2 to get 2/3, with the integer part, 0, serving as the third binary digit. The fractional part is 2/3.\n Finally, multiply 2/3 by 2 to get 4/3. The integer part, 1, is the fourth binary digit. The fractional part is 1/3 again.\n So the first four binary digits of 1/3 are 0.0101.
02

Part (b): Identify Recurring Fraction

By continuing with the process begun in part (a), you'll find that the binary fraction keeps on being .0101 recurring, so the binary representation of 1/3 is 0.010101..., continuing indefinitely.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

If \(a, b \in \mathbb{R}\), prove the following. \(\Rightarrow 1,1-2\) (a) If \(a+b=0\), then \(b=-a, \quad 4\) b, 4 (b) \(-(-a)=a\) (c) \((-1) a=-a\), (d) \((-1)(-1)=1 .\)

If \(u>0\) is any real number and \(x

Find all \(x \in \mathbb{R}\) that satisfy the inequality \(4<|x+2|+|x-1|<5\).

Prove the following form of Theorem 2.1.9: If \(a \in \mathbb{R}\) is such that \(0 \leq a \leq \varepsilon\) for every \(\varepsilon>0\), then \(a=0\)

(a) Show that if \(a>0\), then \(1 / a>0\) and \(1 /(1 / a)=a\). (b) Show that if \(a
See all solutions

Recommended explanations on Math Textbooks

Logic and Functions

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Statistics

Read Explanation

Applied Mathematics

Read Explanation

Decision Maths

Read Explanation

Calculus

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.