To add the binary numbers $10110$ and $111001$, follow these steps:

1. Align the numbers by their least significant bit (rightmost digit), padding the smaller number with zeros at the beginning: $00010110 \quad \text{(binary for 22)}$ $111001 \quad \text{(binary for 57)}$

2. Perform binary addition, remembering the rules:

   • $0 + 0 = 0$
   • $0 + 1 = 1$
   • $1 + 1 = 10$ (write $0$, carry $1$)
   • $1 + 1 + 1 = 11$ (write $1$, carry $1$)

   Adding step by step:

     Carry:   1  1  1  0  0
     Numbers: 0  0  0  1  0  1  1  0
              + 1  1  1  0  0  1
     Result:  1  0  0  0  0  1  1
   

3. The result is $1000011$ in binary.

Final Answer:

The sum of $10110$ and $111001$ in binary is $1000011$, which equals $67$ in decimal.

Would you like more details or further assistance? Here are some related questions to explore:

1. How do you subtract binary numbers?
2. Can you explain binary multiplication?
3. How is binary addition applied in computer science?
4. What is the difference between binary and hexadecimal addition?
5. How do you convert binary to decimal manually?

Tip: When adding binary numbers, align them carefully and work from the rightmost bit to avoid errors with carries.