StudySmarter AI is coming soon!

:00Days
:00Hours
:00Mins
00Seconds

A new era for learning is coming soonSign up for free

Log In Start studying!

Select your language

Suggested languages for you:

Deutsch (DE)

Deutsch (UK)

Deutsch (US)

Americas

English (US)

Europe

Q6RE

Expert-verified

Discrete Mathematics and its Applications

Found in: Page 307

Book edition 7th

Author(s) Kenneth H. Rosen

Pages 808 pages

ISBN 9780073383095

Answers without the blur.

Just sign up for free and you're in.

Register for Free I’ll do it later

Short Answer

Convert $(7206)_{8} and (A 0 EB)_{16}$ to a binary representation

$(111010000110)_{2}$

$(1010000011101011)_{2}$

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1

$(7206)_{8} = 7 * 8^{3} + 2 * 8^{2} + 6 * 8^{0} = (2^{2} + 2^{1} + 2^{0}) 2^{9} + 2^{1} * 2^{6} + (2^{2} + 2^{1}) 2^{0} = 2^{11} + 2^{10} + 2^{9} + 2^{7} + 2^{2} + 2^{1} = (111010000110)_{2}$

Step 2

$(A 0 EB)_{16} = 10 * 16^{3} + 14^{*} 16^{1} + 11^{*} 16^{0} = (2^{3} + 2^{1}) 2^{1} 2 + (2^{3} + 2^{2} + 2^{1}) 2^{4} + (2^{3} + 2^{1} + 2^{0}) 2^{0} = 2^{15} + 2^{13} + 2^{6} + 2^{5} + 2^{3} + 2^{1} + 2^{0} = (1010000011101011)_{2}$

Most popular questions for Math Textbooks

a) How can you find a linear combination (with integer coefficients) of two integers that equals their greatest common divisor?

b) Express $\gcd (84, 119)$ as a linear combination of $84 and 119$ .

Answer Exercise 37 for two's complement expansion.

How is the one's complement representation of the sum of two integers obtained from the one's complement representations of these integers?

Show that every positive integer can be represented uniquely as the sum of distinct powers of 2 . [Hint: Consider binary expansions of integers.]

State the fundamental theorem of arithmetic.

Give a procedure for converting from the hexadecimal expansion of an integer to its octal expansion using binary notation as an intermediate step.

Want to see more solutions like these?

Sign up for free to discover our expert answers

Get Started - It’s free

Recommended explanations on Math Textbooks

94% of StudySmarter users get better grades.

Sign up for free

Find Study Materials for

Create Study Materials

Select your language

Discrete Mathematics and its Applications

Answers without the blur.

Short Answer

Convert $(7206)_{8} and (A 0 EB)_{16}$ to a binary representation

Step by Step Solution

Step 1

Step 2

Most popular questions for Math Textbooks

Want to see more solutions like these?

Recommended explanations on Math Textbooks

Select your language

Discrete Mathematics and its Applications

Answers without the blur.

Short Answer

Convert (7206)8 and (A0EB)16 to a binary representation

Step by Step Solution

Step 1

Step 2

Most popular questions for Math Textbooks

Want to see more solutions like these?

Recommended explanations on Math Textbooks

Decision Maths

Calculus

Probability and Statistics

Statistics

Mechanics Maths

Geometry

Pure Maths

Convert $(7206)_{8} and (A 0 EB)_{16}$ to a binary representation