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Python program to convert Base 4 system to binary number

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Given a base 4 number N, the task is to write a python program to print its binary equivalent.

Conversion Table:


Input       : N=11002233
Output      : 101000010101111
Explanation : From that conversion table we changed 1 to 01, 2 to 10 ,3 to 11 ,0 to 00.
Input : N=321321
Output: 111001111001

Method 1:

  • Take an empty string say resultstr.
  • We convert the decimal number to string.
  • Traverse the string and convert each character to an integer
  • If the integer is 1 or 0 then before converting to binary add ‘0’ to resultstr (Because we cannot have 01,00 in integers)
  • Now convert this integer to binary string and concatenate the resultant binary string to resultstr.
  • Convert resultstr to integer(which removes leading zeros).
  • Return resultstr.

Below is the implementation of the above approach as follows:


# function which converts decimal to binary
def decToBin(num):
    # Using default binary conversion functions
    binary = bin(num)
    # removing first two character as the
    # result is always in the form 0bXXXXXXX
    # by taking characters after index 2
    binary = binary[2:]
    return binary
# function to convert base4 to binary
def convert(num):
    # Taking a empty string
    resultstr = ""
    # converting number to string
    numstring = str(num)
    # Traversing string
    for i in numstring:
        # converting this character to integer
        i = int(i)
        # if i is 1 or 0 then add '0' to result
        # string
        if(i == 1 or i == 0):
            resultstr = resultstr+'0'
        # passing this integer to get converted to
        # binary
        binary = decToBin(i)
        # print(binary)
        # Concatenating this binary string to result
        # string
        resultstr = resultstr+binary
    # Converting resultstr to integer
    resultstr = int(resultstr)
    # Return result string
    return resultstr
# Driver code
Number = 11002233
# Passing this number to convert function




Time Complexity: O(n), Auxiliary Space: O(1)

Here n is the length of the no

Method 2:

Step-by-step approach:

  • The base4_to_binary function takes a string num representing a number in base 4 as input.
  • The function first converts the number to base 10 by multiplying each digit in the number by 4 raised to the power of its position (i.e., the rightmost digit is in position 0, the next digit is in position 1, and so on). This is done by iterating through the digits of the number in reverse order and adding the product of the digit and 4 raised to the power of its position to a variable base10.
  • The function then converts the number from base 10 to binary using the built-in bin() function in Python. The bin() function returns a string with a ‘0b’ prefix, so we slice off the first two characters to get the binary representation of the number as a string.
  • The function returns the binary representation of the number as a string.


def base4_to_binary(num):
    # Convert the number to base 10
    base10 = 0
    for i, digit in enumerate(num[::-1]):
        base10 += int(digit) * (4 ** i)
    # Convert the number to binary
    binary = bin(base10)[2:]
    return binary
num = "11002233"
binary = base4_to_binary(num)
print(f"The binary representation of {num} is {binary}")
# Output: The binary representation of 1032 is 10011010
num = "321321"
binary = base4_to_binary(num)
print(f"The binary representation of {num} is {binary}")
# Output: The binary representation of 30 is 11110


The binary representation of 11002233 is 101000010101111
The binary representation of 321321 is 111001111001

Time complexity: O(n)
Auxiliary Space: O(1)

Last Updated : 20 Mar, 2023
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