Binary Addition
You are given two binary numbers as strings. Your task is to write a program to add these two binary numbers and output the sum as a binary string.
Input
The first line contains the first binary string
a (1 ≤ |a| ≤ 10,000).The second line contains the second binary string
b (1 ≤ |b| ≤ 10,000).Output
Print the sum of the two binary numbers
a + b as a binary string.Examples
Input | Output |
1101
1011 | 11000 |
101
11 | 1000 |
Tutorial on Binary Addition
Just like with decimal numbers, you can perform operations like addition with binary numbers. Binary addition is similar to decimal addition but simpler—there are only four rules to remember:
0 + 0 = 0
1 + 0 = 1
0 + 1 = 1
1 + 1 = 10(which means 0 carry 1, just like10in decimal means 0 carry 1 to the next higher place)
Example of Binary Addition
Let's add
101 and 110: ←←←← The order of operations is from right to left
101
+ 110
------
1011 Result is 1011 in binary, which is 11 in decimal.Start adding from the right:
1 + 0 = 1
0 + 1 = 1
1 + 1 = 10(write 0, carry 1)
- Add the carried-over 1 to the leftmost column.
Constraints
Time limit: 2 seconds
Memory limit: 512 MB
Output limit: 1 MB