Negative base numbers
Negative base numbers are an alternatively way to encode numbers without the need for a minus sign. Various negative bases may be used including negadecimal (base -10), negabinary (-2) and negaternary (-3).[1][2]
- Task
- Encode the decimal number 10 as negabinary
- Encode the decimal number 146 as negaternary (expect 21102)
- Encode the decimal number 15 as negadecimal (expect 195)
- In each of the above cases, convert the encoded number back to decimal.
Perl 6
Perl 6 provides built-in methods base and parse-base to convert to and from bases 2 through 36. We'll just augment the core methods to accept negative bases. We'll simplify things by only dealing with negative bases from -2 through -10.
<lang perl6>use MONKEY-TYPING; # We're messing around with core types
augment class Int {
multi method base (Int $radix where -11 < * < -1) { my @result = self.polymod($radix xx *); for @result.kv -> $k, $v { if $v < 0 { @result[$k ] -= $radix; @result[$k + 1] += 1; } } + flip [~] @result; }
multi method parse-base (Int $radix where -11 < * < -1) { [+] self.flip.comb.kv.map: { $^v * $radix ** $^k } }
}
- TESTING
say ' 10.base( -2) = ', 10.base(-2); say '146.base( -3) = ', 146.base(-3); say ' 15.base(-10) = ', 15.base(-10);
say '11110.parse-base( -2) = ', 11110.parse-base(-2); say '21102.parse-base( -3) = ', 21102.parse-base(-3); say ' 195.parse-base(-10) = ', 195.parse-base(-10);</lang>
- Output:
10.base( -2) = 11110 146.base( -3) = 21102 15.base(-10) = 195 11110.parse-base( -2) = 10 21102.parse-base( -3) = 146 195.parse-base(-10) = 15
Python
<lang python>#!/bin/python from __future__ import print_function
def EncodeNegBase(n, b): #Converts from decimal if n == 0: return "0" out = [] while n != 0: n, rem = divmod(n, b) if rem < 0: n += 1 rem -= b out.append(rem) return "".join(map(str, out[::-1]))
def DecodeNegBase(nstr, b): #Converts to decimal if nstr == "0": return 0
total = 0 for i, ch in enumerate(nstr[::-1]): total += int(ch) * b**i return total
if __name__=="__main__":
print ("Encode 10 as negabinary (expect 11110)") result = EncodeNegBase(10, -2) print (result) if DecodeNegBase(result, -2) == 10: print ("Converted back to decimal") else: print ("Error converting back to decimal")
print ("Encode 146 as negaternary (expect 21102)") result = EncodeNegBase(146, -3) print (result) if DecodeNegBase(result, -3) == 146: print ("Converted back to decimal") else: print ("Error converting back to decimal")
print ("Encode 15 as negadecimal (expect 195)") result = EncodeNegBase(15, -10) print (result) if DecodeNegBase(result, -10) == 15: print ("Converted back to decimal") else: print ("Error converting back to decimal")</lang>
- Output:
Encode 10 as negabinary (expect 11110) 11110 Converted back to decimal Encode 146 as negaternary (expect 21102) 21102 Converted back to decimal Encode 15 as negadecimal (expect 195) 195 Converted back to decimal
References
- ↑ Negabinary on Wolfram Mathworld
- ↑ Negative base on Wikipedia