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Calculate 3310base 5 - 1442base 5

+2 votes
asked Feb 27, 2013 in BASIC MATH by Afeez Novice

1 Answer

+1 vote
 
Best answer

It’s base number problem.

 First convert base 5 to base 10.

 33105 = (3 · 53+ 3 · 52+ 1 · 51 + 0  · 50)10 = 45510

 14425 = (1 · 53+ 4 · 52+ 4 · 51 + 2  · 50)10 = 24710

 33105 -  14425 =  45510  - 24710 = 20810

 Next Convert base 208 base 10 into base 5.

 208 = a0 + 5a1 + 25a2 + 125 a3 + 625 a4 + 3125a5.

where all the are ai digits from 0 to 4. Obviously, all the ai from a4 and up  are 0 since otherwise they will add in a number greater than 208, and all the terms in the sum are nonnegative. Then, we wish to find the largest a3 such that 125a3 does not exceed 208. Thus, a3 = 1 since 1a3 = 125 and 2a3 = 250.

 This leaves us with 208 = a0 + 5a1 + 25a2 + 125(1) à 83 = a0 + 5a1 + 25a2

 83 = a0 + 5a1 + 25(3)à 8 = a0 + 5a1

 8 = a0 + 5 (1) à a0 = 3

 a0  = 3, a1  = 1, a2  = 3 and a3 = 1

 208 10= 13135.

 Let's check by converting answer back into base 10. We know that

 13135 = (1 · 53+ 3 · 52+ 1 · 51 + 3 · 50)10 = 125 + 75 + 5 + 3 = 208.

 

33105  - 14425 = 208 10= 13135.

I hope it helps a lil.

answered Feb 28, 2013 by steve Scholar
selected Mar 1, 2013 by Afeez

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