Python program to add two binary numbers

Given two binary numbers, write a Python program to compute their sum.

Examples:

Input:  a = "11", b = "1"
Output: "100"

Input: a = "1101", b = "100"
Output: 10001

Approach:

• Naive Approach: The idea is to start from the last characters of two strings and compute digit sum one by one. If the sum becomes more than 1, then store carry for the next digits.
• Using inbuilt function: Calculate the result by using the inbuilt bin() and int() function.

Method 1: Naive Approach: 

The idea is to start from the last characters of two strings and compute digit sum one by one. If the sum becomes more than 1, then store carry for the next digits.

Python3

# Python program to add two binary numbers.

# Driver code
# Declaring the variables
a = "1101"
b = "100"
max_len = max(len(a), len(b))
a = a.zfill(max_len)
b = b.zfill(max_len)

# Initialize the result
result = ''

# Initialize the carry
carry = 0

# Traverse the string
for i in range(max_len - 1, -1, -1):
    r = carry
    r += 1 if a[i] == '1' else 0
    r += 1 if b[i] == '1' else 0
    result = ('1' if r % 2 == 1 else '0') + result

    # Compute the carry.
    carry = 0 if r < 2 else 1

if carry != 0:
    result = '1' + result

print(result.zfill(max_len))

Output

10001

Time complexity : O(n)

Space Complexity : O(n) 

Method 2: Using inbuilt functions:

We will first convert the binary string to a decimal using int() function in python. The int() function in Python and Python3 converts a number in the given base to decimal. Then we will add it and then again convert it into a binary number using bin() function.

Example 1:

Python3

# Python program to add two binary numbers.

# Driver code
# Declaring the variables
a = "1101"
b = "100"

# Calculating binary value using function
sum = bin(int(a, 2) + int(b, 2))

# Printing result
print(sum[2:])

Output

10001

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

Example 2:

Python3

# Python program to add two binary numbers.

# Driver code
if __name__ == "__main__" :

    # Declaring the variables
    a = "1101"
    b = "100"

    # Calculating binary sum by using bin() and int()
    binary_sum = lambda a,b : bin(int(a, 2) + int(b, 2))

    # calling binary_sum lambda function
    print(binary_sum(a,b)[2:])

    # This code is contributed by AnkThon

Output

10001

Time complexity :  O(1)

Space Complexity : O(1)

Method: Using “add” operator 

Python3

from operator import*
num1="1101"
num2="100"
print(bin(add(int(num1,2),int(num2,2))))

Output 

0b10001

Time complexity :  O(n)

Space Complexity : O(1)