2421 code

Question

in 2421 code for 5 is 1011 why not 0101 ?????????

Comments

Shaik Masthan

 Can you provide any reference for this? because i have read that some codes are considered invalid in 2421 so there is no choice for representing one number in more than 1 way. We have to represent 5 as 1011.

Max no. that can be represented is 9.

base-10 | 2421-code
     0    |  0000
     1    |  0001
     2    |  0010
     3    |  0011
     4    |  0100
          |
     5    |  1011
     6    |  1100
     7    |  1101
     8    |  1110
     9    |  1111


All you need to remember to work with 2421 code is to name it H421:
the first digit represents the half in which the digit belongs.  The 
next three digits are the standard representation (in 421) of what's
left to transform. 

Ref:http://mathforum.org/library/drmath/view/67281.html

What it says is 2421 is seen as H421 (we write H in place of 2 in MSB..it indicates to which half a number belongs.. 0-4 in 1st half and 5-9 in 2nd..weight of H is 2)

For eg: 6 belongs to the 2nd half so we write H=1. Now how much is left to be added? 6-2=4(since weight of H is 2). So we write 100 for 421. H421 becomes 1100.

3 belongs to 1st half so write H=0. Now how much is left to be added? 3-0=3 only. So we write 011 for 421. H421 becomes 0011 (and not 1001)

5 belongs to 2nd half so write H=1. Now how much is left to be added? (5-2)=3. So we write 011 for 421. H421 becomes 1011.

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Actually

2421 is a self complementary weighted code

and this property satisfying both the case

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@MiNiPanda

One might think that double codes are possible for a number, for example 1011 and 0101 could represent 5. However, here one makes sure that the digits 0 to 4 are mirror image complementary to the numbers 5 to 9.

This is from wiki https://en.wikipedia.org/wiki/Aiken_code

they are saying that  " one makes sure that the digits 0 to 4 are mirror image complementary to the numbers 5 to 9. " ====> no rule that 4 should be treated as 0100

but normally people prefer it.

Answer 1

4 and 5 is not applicable on 2421 as in order to become self complimenting code the 9's can be obtained by toggling the binary bits which is applicable for Decimal  0-3 and 7-10 . ( I am excluding 6 as per the code structure ).

The above concept is supersorted in Excess 3 as all the criteria is met .