N Notation For Python

2021-07-28

about binary, decimal, octal and hex conversion for Python

파이썬으로 2진법 8진법 10진법 16진법 변환, korean version

Notation

  • binary and decimal conversion

    binary → decimal : The multiplier of 2 increases by one

    $1010101(2) -> 2^6 + 2^4 + 2^2 + 2^0 = 64 + 16 + 4 +1 = 85$

    decimal → binary : Divide by 2 each time 85
    = (42)2 + 1 = 85
    = (21)
    2 + 0 = 42
    = (10)2 + 1 = 21
    = (5)
    2 + 0 = 10
    = (2)2 + 1 =5
    =(1)
    2 + 0 = 2
    =(0)*2 + 1 = 1
    → 1010101

      #2->10
    
      def binary_to_decimal(binary):
          decimal = 0
          temp = list(str(binary))
          length = len(temp)
          for i, e in enumerate(temp):
              if e == '1': decimal += 2**(length -1 - i)
          return int(decimal)
    
      #10->2
      def decimal_to_binary(decimal):
          temp = deque()
          q,r = divmod(int(decimal), 2)
          temp.appendleft(r)
          while q != 0:
              q,r = divmod(q, 2)
              temp.appendleft(r)
          binary = ''.join(list(map(str, temp)))
          return str(binary)
    
  • binary and hex conversion

    binary → hex

    \[1110011011(2) -> 0011/1001/1011\] \[2^1+2^0/2^3+2^0/2^3+2^1+2^0 = 3/9/11 =0x39B\]

    hex → binary

    \[0x39B → 3/9/B\] \[11/1001/1011\]
      #2->16
      def binary_to_hexadecimal(binary):
          binary = list(str(binary))
          for _ in range(4 - len(binary)%4):
              binary.insert(0, 0) 
          answer = deque()
          t = 0
          temp = 0
          while binary:
              n = int(binary.pop())
              if n == 1:
                  temp += 2**t
              t+=1
              if t = 4:
                  if temp >=10:
                      temp += 55
                      answer.appendleft(chr(temp))
                  else:answer.appendleft(str(temp))
                  t = 0
                  temp = 0
          answer.appendleft('0x')
          answer = ''.join(answer)
          return str(answer)
    
      #16->2
      def hexadecimal_to_binary(hexadecimal):
          answer = []
          temp = list(hexadecimal[2:])
          for e in temp:
              if e.isalpha(): n = ord(e) - 55
              else: n = int(e)
              n = str(decimal_to_binary(n))
              while len(n) != 4:
                  n=''.join(['0', n])
              answer.append(n)
          answer = ''.join(answer)
          answer = answer.lstrip('0')
          return str(n)
    
  • decimal and hex conversion

    decimal → hex

    10 = A
    11 = B
    12 = C
    13 = D
    14 = E
    15 = F

    127 = (7)16 + 15 = (0)16 + 7 → 0x7F

    hex -> decimal

    \[7F -> 16^1*7 +16^0*15 = 112 + 15 =127\]
      #10->16
      def decimal_to_hexadecimal(decimal):
          answer = []
          temp = deque()
          q,r = divmod(int(decimal), 16)
          temp.appendleft(r)
    
          while q != 0:
              q,r = divmod(q, 2)
              temp.appendleft(r)
          for e in temp:
              if e >=10:
                      e += 55
                      answer.appendleft(chr(e))
              else:answer.appendleft(str(e))
                
          answer.appendleft('0x')
          hexadecimal = ''.join(answer)
          return str(hexadecimal)
            
      #16->10
      def hexadecimal_to_decimal(hexadecimal):
          answer = 0
          hexa = list(hexadecimal[2:].upper())
          length = len(hexa)
          for i,e in enumerate(hexa):
              if e.isalpha(): answer += (ord(e)-55)*(16**(length-1-i))
              else: answer += (16**(length-1-i))*int(e)
          return int(answer)
    

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