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.
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.
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.
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.
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.
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.
Therefore, the equivalent value of
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.
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.
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.
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.
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.
Therefore, the equivalent value of
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.
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.
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.
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.
Therefore, the equivalent value of
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.
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.
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.
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
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Essentials of Computer Organization and Architecture
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