Essentials of Computer Organization and Architecture
Essentials of Computer Organization and Architecture
5th Edition
ISBN: 9781284123036
Author: Linda Null
Publisher: Jones & Bartlett Learning
Expert Solution & Answer
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Chapter 2, Problem 2E

Explanation of Solution

a)

Converting 588 base 10 to base 3 using subtraction method:

Step 1:

Check the possibility of multiplying any integer with the powers of 3 which may result in lower number than 588. The number that can be subtracted from the given number 588 with the power of 3 is 243 and it should be multiplied by 2 in order to get the nearest number of 588. The number 486 is less than 588. So subtract 486 from 588.

588-486=35x2------------102

Step 2:

The number that can be subtracted from the given number 102 with the power of 3 is 81. The number 81 is less than 102. So subtract 81 from 102.

102-81=34x1------------21

Step 3:

Take 3 to the power of 3 that is 27. The number 27 is greater than 21. So make the value as 0.

21-0=33x0------------21

Step 4:

The number that can be subtracted from the given number 21 with the power of 3 is 9 and it should be multiplied by 2 in order to get the nearest number of 21. The number 18 is less than 21. So subtract 18 from 21.

21-18=32x2------------3

Step 5:

The number that can be subtracted from the given number 3 with the power of 3 is 3. So subtract 3 from 3.

3-3=31x1------------0

Step 6:

Take 3 to the power of 0 that is 1. So make the value as 0. The result will be 0. The process is stopped as the remainder is 0.

0-0=30x0------------0

Therefore, the equivalent value of 58810 is “2102102”.

Explanation of Solution

b)

Converting 2254 base 10 to base 5 using subtraction methods:

Step 1:

Check the possibility of multiplying any integer with the powers of 5 which may result in lower number than 2254. The number that can be subtracted from the given number 2254 with the power of 5 is 625 and it should be multiplied by 3 in order to get the nearest number of 2254. The number 1875 is less than 2254. So subtract 1875 from 2254.

2254-1875=54x3------------379

Step 2:

The number that can be subtracted from the given number 379 with the power of 5 is 125 and it should be multiplied by 3 in order to get the nearest number of 379. The number 375 is less than 379. So subtract 375 from 379.

379-375=53x3------------4

Step 3:

Take 5 to the power of 2 that is 25. The number 25 is greater than 4. So make the value as 0.

4-0=52x0------------4

Step 4:

Take 5 to the power of 1 that is 5. The number 5 is greater than 4. So make the value as 0.

4-0=51x0------------4

Step 5:

The number that can be subtracted from the given number 4 with the power of 5 is 1 and it should be multiplied by 4 in order to get the nearest number of 4. So subtract 4 from . The result will be 0. The process is stopped as the remainder is 0.

4-4=51x4------------0

Therefore, the equivalent value of 225410 is “330042”.

Explanation of Solution

c)

Converting 652 base 10 to base 7 using subtraction method:

Step 1:

Check the possibility of multiplying any integer with the powers of 7 which may result in lower number than 652. The number that can be subtracted from the given number 652 with the power of 7 is 343. The number 343 is less than 652. So subtract 343 from 652.

652-343=73x1------------309

Step 2:

The number that can be subtracted from the given number 309 with the power of 7 is 49 and it should be multiplied by 6 in order to get the nearest number of 309. The number 294 is less than 309. So subtract 294 from 309.

309-294=72x6------------15

Step 3:

The number that can be subtracted from the given number 15 with the power of 7 is 7 and it should be multiplied by 2 in order to get the nearest number of 15. The number 14 is less than 15. So subtract 14 from 15.

15-14=71x2------------1

Step 4:

The number that can be subtracted from the given number 1 with the power of 7 is 1. So subtract 1 from 1. The result will be 0. The process is stopped as the remainder is 0.

1-1=70x1------------0

Therefore, the equivalent value of 65210 is “16212”.

Explanation of Solution

d)

Converting 3104 base 10 to base 9 using subtraction methods:

Step 1:

Check the possibility of multiplying any integer with the powers of 9 which may result in lower number than 3104. The number that can be subtracted from the given number 3104 with the power of 9 is 729 and it should be multiplied by 4 in order to get the nearest number of 3104. The number 2916 is less than 3104. So subtract 2916 from 3014.

3104-2916=93x4------------188

Step 2:

The number that can be subtracted from the given number 188 with the power of 9 is 81 and it should be multiplied by 2 in order to get the nearest number of 188. The number 162 is less than 188. So subtract 162 from 188.

188-162=92x2------------26

Step 3:

The number that can be subtracted from the given number 26 with the power of 9 is 9 and it should be multiplied by 2 in order to get the nearest number of 26. The number 18 is less than 26. So subtract 18 from 26.

26-8=91x2------------8

Step 4:

The number that can be subtracted from the given number 8 with the power of 9 is 1 and it should be multiplied by 8 in order to get the nearest number of 8. So subtract 8 from 8. The result will be 0. The process is stopped as the remainder is 0.

Therefore, the equivalent value of 310410 is “42282”.

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Chapter 2 Solutions

Essentials of Computer Organization and Architecture

Ch. 2 - Prob. 11RETCCh. 2 - Prob. 12RETCCh. 2 - Prob. 13RETCCh. 2 - Prob. 14RETCCh. 2 - Prob. 15RETCCh. 2 - Prob. 16RETCCh. 2 - Prob. 17RETCCh. 2 - Prob. 18RETCCh. 2 - Prob. 19RETCCh. 2 - Prob. 20RETCCh. 2 - Prob. 21RETCCh. 2 - Prob. 22RETCCh. 2 - Prob. 23RETCCh. 2 - Prob. 24RETCCh. 2 - Prob. 25RETCCh. 2 - Prob. 26RETCCh. 2 - Prob. 27RETCCh. 2 - Prob. 28RETCCh. 2 - Prob. 29RETCCh. 2 - Prob. 30RETCCh. 2 - Prob. 31RETCCh. 2 - Prob. 32RETCCh. 2 - Prob. 33RETCCh. 2 - Prob. 34RETCCh. 2 - Prob. 1ECh. 2 - Prob. 2ECh. 2 - Prob. 3ECh. 2 - Prob. 4ECh. 2 - Prob. 5ECh. 2 - Prob. 6ECh. 2 - Prob. 7ECh. 2 - Prob. 8ECh. 2 - Prob. 9ECh. 2 - Prob. 10ECh. 2 - Prob. 11ECh. 2 - Prob. 12ECh. 2 - Prob. 13ECh. 2 - Prob. 14ECh. 2 - Prob. 15ECh. 2 - Prob. 16ECh. 2 - Prob. 17ECh. 2 - Prob. 18ECh. 2 - Prob. 19ECh. 2 - Prob. 20ECh. 2 - Prob. 21ECh. 2 - Prob. 22ECh. 2 - Prob. 23ECh. 2 - Prob. 24ECh. 2 - Prob. 25ECh. 2 - Prob. 26ECh. 2 - Prob. 27ECh. 2 - Prob. 29ECh. 2 - Prob. 30ECh. 2 - Prob. 31ECh. 2 - Prob. 32ECh. 2 - Prob. 33ECh. 2 - Prob. 34ECh. 2 - Prob. 35ECh. 2 - Prob. 36ECh. 2 - Prob. 37ECh. 2 - Prob. 38ECh. 2 - Prob. 39ECh. 2 - Prob. 40ECh. 2 - Prob. 41ECh. 2 - Prob. 42ECh. 2 - Prob. 43ECh. 2 - Prob. 44ECh. 2 - Prob. 45ECh. 2 - Prob. 46ECh. 2 - Prob. 47ECh. 2 - Prob. 48ECh. 2 - Prob. 49ECh. 2 - Prob. 50ECh. 2 - Prob. 51ECh. 2 - Prob. 52ECh. 2 - Prob. 53ECh. 2 - Prob. 54ECh. 2 - Prob. 55ECh. 2 - Prob. 56ECh. 2 - Prob. 57ECh. 2 - Prob. 58ECh. 2 - Prob. 59ECh. 2 - Prob. 60ECh. 2 - Prob. 61ECh. 2 - Prob. 62ECh. 2 - Prob. 63ECh. 2 - Prob. 64ECh. 2 - Prob. 65ECh. 2 - Prob. 66ECh. 2 - Prob. 67ECh. 2 - Prob. 68ECh. 2 - Prob. 69ECh. 2 - Prob. 70ECh. 2 - Prob. 71ECh. 2 - Prob. 72ECh. 2 - Prob. 73ECh. 2 - Prob. 74ECh. 2 - Prob. 75ECh. 2 - Prob. 76ECh. 2 - Prob. 77ECh. 2 - Prob. 78ECh. 2 - Prob. 79ECh. 2 - Prob. 80ECh. 2 - Prob. 81ECh. 2 - Prob. 82E
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