Question

Recall your earlier knowledge represent 555 in base 5

Answer 1

3 to the power 5..........

Answer 2

SOLUTION----------

Whenever you have to convert a number X in a base B we follow the following procedure.

First, we need to know that in a base B number allowed digits are from 0 to B-1. For example, in base 10 we use digits from 0 to 9. So, in this question, allowed digits would be from 0 to 4.

Following is a correspondence between decimal (means base 10 numbers) and base-5 numbers:

base-10 number       base-5 number

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0                                    0

1                                     1

2                                    2

3                                    3

4                                    4

5                                    10 (Since 5 is not an allowed digit in base-5)

6                                    11

7                                    12

8                                    13

9                                    14

10                                   20 (again, we can't write 15 in base-5)

and so on.

Humans understand decimal better, so there is a way to convert a base-B number to base-10, which follows:

If an n-digit number in base-5 is:

Then it's expanded to decimal as follows:

So to convert the decimal number back to base-B, we follow the procedure the repeated division of number and writing the remainder in each step from right to left.

eg: 

555/5=111    = 0

111/5=22     = 1

22/5=4       = 2

4/5=0         = 4

Writing as  , the decimal number 555 is written as 4210 in base-5.