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2421 Decimal Code

Date: 11/08/2004 at 04:23:28
From: Dibyendu
Subject: 2421 decimal code

Can you explain why some bit combinations for 2421 are invalid?  For 
example, to represent decimal 5 (five) in 2421, the correct code is 
1011.  But why can't we represent decimal 5 in 2421 as 0101, because 
if we add the weights as 0*2 + 1*4 + 0*2 + 1*1, we get 5 in decimal. 

The most confusing part is that some decimal numbers can have multiple 
representations in 2421 but only one among them is treated as a valid 
code.  Why?



Date: 11/08/2004 at 11:56:50
From: Doctor Cristian
Subject: Re: 2421 decimal code

Hi Dibyendu, and thanks for writing to Dr. Math!

I found the table of the 2421 representation of digits by searching 
the Internet for these keywords:

  2421 decimal code

It goes as follows:

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

It seems to me that when the code was invented, they wanted an x421 
code that can start at 0000 and end at 1111 (which determines the 
value of x: x = 9 - 4 - 2 - 1 = 2). The halves would be easy to 
divide: the first five digits start with 0, the last five digits start
with 1. 

So 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: n - (2 * first_digit).

In fact, all the digits between 2 and 7 (inclusive) have multiple 
representations in 2421, but that doesn't stop anyone from passing the 
2421 code along.  :^D

Does this help?

- Doctor Cristian, The Math Forum
  http://mathforum.org/dr.math/ 



Date: 11/09/2004 at 09:14:01
From: Dibyendu
Subject: Thank you (2421 decimal code)

Thank you so much.  Keep up the good work.
Associated Topics:
Elementary Number Sense/About Numbers
Elementary Place Value
Middle School Number Sense/About Numbers

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