landscape Posted July 21, 2012 Share Posted July 21, 2012 Find the value of x if (23)_{x }= 111100010_{2} I've converted it into decimal, which is 482. But that's where I get stuck. Any ideas? Link to comment Share on other sites More sharing options...

imatfaal Posted July 23, 2012 Share Posted July 23, 2012 You need to break down 23 or any number in a place-holder system. The number 576 in decimal is interpreted without thinking - but what does it represent? [math] 576_{10} = (5*10^2) + (7*10^1) + (6 *10^0) [/math] in general [math] 576_x = (5*x^2) + (7*x^1) + (6 *x^0) [/math] You can then just rearrange your question into a nice polynomial which you solve for x. That said I must be missing something cos I cannot get yours to work - maybe I am just having a brain fade. Link to comment Share on other sites More sharing options...

Schrödinger's hat Posted July 24, 2012 Share Posted July 24, 2012 (edited) Imfataal, the reason you're having trouble is: Assuming his radix is an integer. [math]23_x = 2x + 3 = 2(x+1) + 1 = 2n+1 [/math] Is odd. [math]111100010_2[/math] is even. Either his radix is not an integer (rational solution to [math]2x+3 = 482[/math]) or there's a transcription error somewhere. Edited July 24, 2012 by Schrödinger's hat 1 Link to comment Share on other sites More sharing options...

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