Given a base 4 number N, the task is to write a python program to print its binary equivalent.
Conversion Table:
Examples:
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:
Python3
# function which converts decimal to binarydef 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 binarydef 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 codeNumber = 11002233# Passing this number to convert functionprint(convert(Number)) |
Output:
101000010101111
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.
Python3
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 binarynum = "11002233"binary = base4_to_binary(num)print(f"The binary representation of {num} is {binary}")# Output: The binary representation of 1032 is 10011010num = "321321"binary = base4_to_binary(num)print(f"The binary representation of {num} is {binary}")# Output: The binary representation of 30 is 11110 |
Output
The binary representation of 11002233 is 101000010101111 The binary representation of 321321 is 111001111001
Time complexity: O(n)
Auxiliary Space: O(1)
