Explanation Given: The given condition is, 986 B 16 Procedure: Steps for converting from base sixteen to base eight is as follows. Step 1: Convert the base sixteen numbers to base two. Step 2: Convert the base two numbers to base eight. Steps for converting from base sixteen to base two is as follows. Step 1: Convert each base sixteen digit to base two. Step 2: Replace each base sixteen digit with a four-digit version of its base two equivalents. Steps for converting from base two to base eight is as follows. Step 1: Break the base two number up into sets of three digits, adding zeros on the left side if necessary. Step 2: Convert each of the base two numbers from step1 to base eight. Step 3: Replace each base two three-digit number with its base eight equivalents. Calculation: Consider the given condition, 986 B 16 The condition is in base sixteen forms. So, first convert it into base two. Now, convert each base sixteen digit to base two. 986 B 16 has three digits 9 16 , 8 16 , 6 16 and B 16 . Value of digit in base ten, 9 16 = 9 Now, expand the above expression. 9 16 = 1 ⋅ 2 3 + 0 ⋅ 2 2 + 0 ⋅ 2 1 + 1 ⋅ 2 0 Then, convert in base two with four digits. 9 16 = 1001 2 Similarly for remaining digits, 8 16 = 8 = 1 ⋅ 2 3 + 0 ⋅ 2 2 + 0 ⋅ 2 1 + 0 ⋅ 2 0 = 1000 2 for digit 6 16 . 6 16 = 6 = 1 ⋅ 2 2 + 1 ⋅ 2 1 + 0 ⋅ 2 0 = 110 2 = 0110 2 And for digit B 16 . B 16 = 11 = 1 ⋅ 2 3 + 0 ⋅ 2 2 + 1 ⋅ 2 1 + 1 ⋅ 2 0 = 1011 2 Now, replace each base eight digit with a four-digit version. 986B 16 = ( 1001 ) ( 1000 ) ( 0110 ) ( 1011 ) = 1001100001101011 2 Now, convert from base two to base eight

8th Edition

ISBN: 9781305104174

Author: David B. Johnson, Thomas A. Mowry

Publisher: Cengage Learning

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Chapter 7.1, Problem 74E

To determine

To find:

The value in base eight for 986B16.

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Chapter 7.1, Problem 73E

Chapter 7.1, Problem 75E

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Chapter 7 Solutions

Mathematics: A Practical Odyssey

Ch. 7.1 - In Exercises 120, write the given number in...Ch. 7.1 - In Exercises 120, write the given number in...Ch. 7.1 - Prob. 3E Ch. 7.1 - Prob. 4E Ch. 7.1 - Prob. 5E Ch. 7.1 - Prob. 6E Ch. 7.1 - Prob. 7E Ch. 7.1 - Prob. 8E Ch. 7.1 - Prob. 9E Ch. 7.1 - Prob. 10E

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