Question

recalling your earlier knowledge,represent 555 in base 5

Answer 1

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
------------------------------------------------------
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:
$a_{n-1} a_{n-2} a_{n-3}... a_{2} a_{1} a_{0}$

Then it's expanded to decimal as follows:
$a_{n-1} * B^{n-1} + a_{n-2}* B^{n-2} + ... + a_{2}* B^{2} +a_{1} * B^{1} + a_{0} * B^{0}$

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   $R_{0}$ = 0
111/5=22     $R_{1}$ = 1
22/5=4       $R_{2}$ = 2
4/5=0        $R_{3}$ = 4

Writing as $R_{3} R_{2} R_{1} R_{0}$ , the decimal number 555 is written as 4210 in base-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
------------------------------------------------------
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.

Hope it helps-------