Negative BasesDate: 05/13/2002 at 14:53:48 From: S. James Subject: Base -2 Dear Sir, I recently ran across a problem where it was desirable to attempt to express a number in base -2 (minus two) format! Just what values might such a base allow? 0 and -1? What would 16 (base 10) then yield as the result of base -2? Thanks, S. James Date: 05/13/2002 at 16:12:03 From: Doctor Peterson Subject: Re: Nth Root, Base -2 Hi, S. See this page in our archives, which I found by searching for the phrase "negative bases": http://mathforum.org/library/drmath/view/55710.html You use digits 0 and 1 for base -2, though I suppose 0 and -1 could be used just as well. To convert, you use the same method as for positive bases, but you have to be careful how you think about remainders. Dividing repeatedly by the base and taking the positive remainders as digits (starting at the right), we convert 10 to base -2 this way: 10 = -2*-5 + 0 -5 = -2*3 + 1 (the quotient is 3 rather than 2 so the remainder is positive) 3 = -2*-1 + 1 -1 = -2*1 + 1 (again, the quotient is NOT 0!) 1 = -2*0 + 1 So 10 (base 10) = 11110 (base -2). I'll let you work out 16 the same way. - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/ |
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