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.
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