N Notation For Python(파이썬 에서의 진법 변환)

about binary, decimal, octal and hex conversion for Python(파이썬으로 2진법 8진법 10진법 16진법 변환)

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

  $$7F -> 16^17 +16^015 = 112 + 15 =127$$

    #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)