A number in Number System of base or radix r is represented by a set of symbols from r distinct symbols .
so Radix means base , like in binary number syatem radix is 2 , they are 0 and 1 .
here radix = 20 , means number is represented by 0-19 .
BCD means to represent a decimal number into it's binary form digit by digit , in BCD or binary-coded-decimal code, a decimal number is not converted as a whole to binary, but rather digit by digit .
like in BCD 4 bits are needed to represent each digit of a binary number , like 2 is represented in BCD as 0010 .
in Excess 3 code 0011( decimal 3) is added with every BCD( decimal digit ) of a number. like excess-3 code for 421 is 754 for 7 0111 , for 5 0101 and for 4 0100 .
If number system uses 20 as radix, each digit needs 5 bits in equivalent Binary number . [ it is because now 25 = 32 , 20 < 32 ] . But to represent a binary number in to BCD we need 4 bits, because BCD implies binary coded decimal 0 to 9. If we consider 5th bit for bcd, we would essentially represent numbers greater than 9 . In BCD we only use the representations from 0 to 9 [3].
Given radix or base is 20 , so number range for base 20 is 0 to 19 .
Now we know that for decimal 0 to 9 binary and BCD representation is same . ex: take 9 it's in binary is 00001001 , BCD representation of 9 is also 00001001 .
Next is decimal range 10 to 19 . For this 10-19 range , lets take number 10 , it is in binary 00001010 . when we convert 10 into BCD for 0 it is 0000 for 1 it is 0001 so BCD for 10 is 00010000 .
00001010 = 10
00010000 = 16 , so excess is 16 - 10 = 6 .
again take 17 , it's binary is 00010001 , BCD is 1 = 0001 & 7 = 0111 .
00010001 = 17
00010111 = 23 so excess is 23 - 17 = 6 .
take last number in this rage that is 19 .
00010011 = 19
00011001 = 25 so excess is 25 - 19 = 6
That's why in range between 10 to 19 we use excess 6 when represent in BCD.
Now we take 20 .
00010100 = 20
00100000 = 32 , so excess is 32 - 20 = 12
if we continue this , we can see that for range 20 to 29 we have to add 12 [1].
In this question , a number system uses radix as 20 , so for radix 20 range of numbers are 0 to 19 ( it is same like for base 10 , range of numbers are 0 to 9 like that )
we can see that for range 0-9 BCD is same as decimal and for range 10-19, we use Excess 6 to represent a number to its equivalent binary coded representation .
when number is 20 we need to use Excess 12 [1].
Hence for radix 20 number system , the excess code that is necessary for its equivalent binary coded representation is 6 .
Btw , This question asks if we have any base 20 number system, then how many excess bits we need when represent any number from this number system into BCD .
Reference:
[1] https://answers.yahoo.com/question/index?qid=20070930062637AAzyBlv
[2] https://www.physicsforums.com/threads/in-bcd-addition-why-add-6.639798/
[3] https://electronics.stackexchange.com/questions/87211/why-do-we-add-6-in-bcd-addition